Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevb.108.125142

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Publishing type：Research paper (scientific journal)   Publisher：Elsevier BV  

DOI： 10.1016/j.softx.2022.101266

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Publishing type：Research paper (scientific journal)   Publisher：Stichting SciPost  

This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions.The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions.A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently.We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal--Eliashberg theory.We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes.This lecture note follows the Japanese review article [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].

DOI： 10.21468/scipostphyslectnotes.63

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevb.106.085114

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.106.085114/fulltext

Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

Analytic continuation (AC) from the imaginary-time Green's function to the spectral function is a crucial process for numerical studies of the dynamical properties of quantum many-body systems. This process, however, is an ill-posed problem; that is, the obtained spectrum is unstable against the noise of the Green's function. Though several numerical methods have been developed, each of them has its own advantages and disadvantages. The sparse modeling (SpM) AC method, for example, is robust against the noise of the Green's function but suffers from unphysical oscillations in the low-energy region. We propose a method that combines the SpM AC with the Padé approximation. This combination, called SpM-Padé, inherits robustness against noise from SpM and low-energy accuracy from Padé, compensating for the disadvantages of each. We demonstrate that the SpM-Padé method yields low-variance and low-biased results with almost the same computational cost as that of the SpM method.

DOI： 10.1103/physrevb.105.035139

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Publishing type：Research paper (scientific journal)   Publisher：Stichting SciPost  

We present a new open-source program, DCore, that implements dynamical mean-field theory (DMFT).
DCore features a user-friendly interface based on text and HDF5 files.
It allows DMFT calculations of tight-binding models to be performed on predefined lattices as well as ab initio models constructed by external density functional theory codes through the Wannier90 package.
Furthermore, DCore provides interfaces to many advanced quantum impurity solvers such as quantum Monte Carlo and exact diagonalization solvers.
This paper details the structure and usage of DCore and shows some applications.

DOI： 10.21468/scipostphys.10.5.117

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In this work, we investigate models for bulk, bi-, and multilayers containing half-metallic ferromagnets (HMFs), at zero and at finite temperature, in order to elucidate the effects of strong electronic correlations on the spectral properties (density of states). Our focus is on the evolution of the finite-temperature many-body induced tails in the half-metallic gap. To this end, the dynamical mean-field theory (DMFT) is employed. For the bulk, a Bethe lattice model is solved using a matrix product states based impurity solver at zero temperature and a continuous-time quantum Monte Carlo (CT-QMC) solver at finite temperature. We demonstrate numerically, in agreement with the analytical result, that the tails vanish at the Fermi level at zero temperature. In order to study multilayers, taken to be square lattices within the layers, we use the real-space DMFT extension with the CT-QMC impurity solver. For bilayers formed by the HMF with a band or correlated insulator, we find that charge fluctuations between the layers enhance the finite-temperature tails. In addition, in the presence of interlayer hopping, a coherent quasiparticle peak forms in the otherwise correlated insulator. In the multilayer heterostructure setup, we find that by suitably choosing the model parameters, the tails at the HMF-Mott insulator interface can be reduced significantly and that a high spin polarization is conceivable, even in the presence of long-ranged electrostatic interactions.

DOI： 10.1103/PhysRevResearch.2.043263

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We formulate an efficient scheme to perform a Migdal-Eliashberg calculation considering the retardation effect from first principles. While the conventional approach requires a huge number of Matsubara frequencies, we show that the intermediate representation of the Green's function [H. Shinaoka et al., Phys. Rev. B 96, 035147 (2017)] dramatically reduces the numerical cost to solve the linearized gap equation. Without introducing any empirical parameter, we obtain a superconducting transition temperature of elemental Nb (similar to 10 K), which is consistent with experiment. The present result indicates that our approach has a superior performance for many superconductors for which T-c is lower than O(10) K.

DOI： 10.1103/PhysRevB.102.134503

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevb.101.125117

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Publishing type：Research paper (international conference proceedings)   Publisher：Journal of the Physical Society of Japan  

DOI： 10.7566/jpscp.30.011005

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Publishing type：Research paper (scientific journal)   Publisher：Stichting SciPost  

Many-body calculations at the two-particle level require a compact
representation of two-particle Green’s functions. In this paper, we
introduce a sparse sampling scheme in the Matsubara frequency domain as
well as a tensor network representation for two-particle Green’s
functions. The sparse sampling is based on the intermediate
representation basis and allows an accurate extraction of the
generalized susceptibility from a reduced set of Matsubara frequencies.
The tensor network representation provides a system independent way to
compress the information carried by two-particle Green’s functions. We
demonstrate efficiency of the present scheme for calculations of static
and dynamic susceptibilities in single- and two-band Hubbard models in
the framework of dynamical mean-field theory.

DOI： 10.21468/scipostphys.8.1.012

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We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Green's function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications. Program summary: Program Title: SpM Program Files doi: http://dx.doi.org/10.17632/ycmpsnv5yx.1 Licensing provisions: GNU General Public License version 3 Programming language: C++. External routines/libraries: BLAS, LAPACK, and CPPLapack libraries. Nature of problem: The analytic continuation of imaginary-time input data to real-frequency spectra is known to be an ill-conditioned inverse problem and very sensitive to noise and the statistic errors. Solution method: By using a modern regularization technique, analytic continuation is made robust against noise since the basis that is unaffected by the noise is automatically selected.

DOI： 10.1016/j.cpc.2019.07.001

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The open-source library, irbasis, provides easy-to-use tools for two sets of orthogonal functions named intermediate representation (IR). The IR basis enables a compact representation of the Matsubara Green's function and efficient calculations of quantum models. The IR basis functions are defined as the solution of an integral equation whose analytical solution is not available for this moment. The library consists of a database of pre-computed high-precision numerical solutions and computational code for evaluating the functions from the database. This paper describes technical details and demonstrates how to use the library. Program summary: Program Title: irbasis Program Files doi: http://dx.doi.org/10.17632/2fh88ynxm6.1 Licensing provisions: MIT license Programming language: C++, Python. External routines/libraries: numpy, scipy and h5py for Python library, HDF5 C library for C++ library. Nature of problem: Numerical orthogonal systems for Green's function Solution method: Galerkin method, piece-wise polynomial representation

DOI： 10.1016/j.cpc.2019.02.006

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Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/PhysRevB.99.165134

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.99.165134/fulltext

DOI： 10.1016/j.cpc.2018.10.025

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.74.1.0_2180

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DOI： 10.1103/PhysRevB.98.035104

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at the two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Green's functions in terms of an overcomplete representation based on the recently proposed "intermediate representation" basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Green's function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.

DOI： 10.1103/PhysRevB.97.205111

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Extensions of dynamical mean-field theory (DMFT) make use of quantum impurity models as nonperturbative and exactly solvable reference systems which are essential to treat the strong electronic correlations. Through the introduction of retarded interactions on the impurity, these approximations can be made two-particle selfconsistent. This is of interest for the Hubbard model because it allows to suppress the antiferromagnetic phase transition in two dimensions in accordance with the Mermin-Wagner theorem, and to include the effects of bosonic fluctuations. For a physically sound description of the latter, the approximation should be conserving. In this paper, we show that the mutual requirements of two-particle self-consistency and conservation lead to fundamental problems. For an approximation that is two-particle self-consistent in the charge and longitudinal spin channels, the double occupancy of the lattice and the impurity is no longer consistent when computed from single-particle properties. For the case of self-consistency in the charge and longitudinal as well as transversal spin channels, these requirements are even mutually exclusive so that no conserving approximation can exist. We illustrate these findings for a two-particle self-consistent and conserving DMFT approximation.

DOI： 10.1103/PhysRevB.96.075155

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR)of analytical continuation. We demonstrate the efficiency of the IR through continuous-time quantum Monte Carlo calculations of an Anderson impurity model. We find that the IR yields a significantly compact form of various types of correlation functions. This allows the direct quantum Monte Carlo measurement of Green's functions in a compressed form, which considerably reduces the computational cost and memory usage. Furthermore, the present framework will provide general ways to boost the power of cutting- edge diagrammatic/quantum Monte Carlo treatments of many-body systems.

DOI： 10.1103/PhysRevB.96.035147

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A data-science approach to solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred real-frequency spectra. By means of a modern regularization technique, we eliminate redundant degrees of freedom that essentially carry the noise, leaving only relevant information unaffected by the noise. The resultant spectrum is represented with minimal bases and thus a stable analytical continuation is achieved. This framework further provides a tool for analyzing to what extent the Monte Carlo data need to be accurate to resolve details of an expected spectral function.

DOI： 10.1103/PhysRevE.95.061302

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

A quantum critical behavior of the magnetic susceptibility was observed in a quasicrystal containing ytterbium. At the same time, a mixed-valence feature of Yb ions was reported, which appears to be incompatible with the magnetic instability. We derive the magnetic susceptibility by expressing the quasiperiodicity as the distributed hybridization strength between Yb 4f and conduction electrons. Assuming a wide distribution of the hybridization strength, the most f electrons behave as renormalized paramagnetic states in the Kondo or mixed-valence regime, but a small number of f moments remain unscreened. As a result, the bulk magnetic susceptibility exhibits a nontrivial power-law-like behavior, while the average f-electron occupation is that of mixed-valence systems. This model thus resolves two contradictory properties of Yb quasicrystals.

DOI： 10.7566/JPSJ.85.073712

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.71.2.0_1868

CiNii Article

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Language：Japanese   Publisher：The Physical Society of Japan  

DOI： 10.11316/jpsgaiyo.71.2.0_2294

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

A modified version of the spinless Anderson model is studied by means of the continuous-time quantum Monte Carlo method. This study is motivated by the peculiar heavy-fermion behavior observed in certain Samarium compounds, which is insensitive to magnetic field. The model involves M channels for conduction electrons, all of which interact with local f electron via the Coulomb repulsion U-fc, while only one channel has hybridization with the local state. The effective hybridization is reduced by the Anderson orthogonality effect, and a quantum critical point occurs with increasing M and/or increasing U-fc. The numerical results at finite temperature of the local charge susceptibility are well fitted by a simple scaling theory for all M. However, the single-particle spectrum is described by a double Lorentzian for M > 1, in contrast with the single Lorentzian with M = 1. A quasi-particle perturbation theory is presented that reproduces the quantum critical point for large M. The quasi-particle theory gives not only the renormalized energy scale, but its extrapolation toward higher energies being consistent with the double Lorentzian spectrum.

DOI： 10.7566/JPSJ.84.104602

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Elsevier B.V.  

Superconductivity in the two-dimensional Kondo lattice model is derived by means of the dual-fermion approach. This framework takes full account of local correlations based on the dynamical mean-field theory and further includes influence of critical antiferromagnetic fluctuations. It is found that pairing with dx2 -y2 symmetry similar to the Hubbard model appears only in the weak-coupling regime. As the coupling is increased, we observe transition to p-wave spin-singlet superconductivity. The emergence of the unconventional p-wave pairing is ascribed to formation of large Fermi surface, which embodies itinerancy of f electrons.

DOI： 10.1016/j.phpro.2015.12.199

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.70.1.0_2475

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.70.2.0_1976

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Language：English   Publishing type：Research paper (scientific journal)  

This paper studies the charge Kondo effect in the (spinless) interacting resonant level model (IRLM) by means of the continuous-time quantum Monte Carlo method. The charge Kondo effect may be relevant to certain Samarium compounds with peculiar heavy-fermion behavior. We use double expansion with respect to Coulomb interaction Uf c and hybridization V. Exact dynamics and thermodynamics of the IRLM are derived numerically for a wide range of Uf c with a given value of V. As Uf c becomes negative, a quantum critical point is found in excellent agreement with a simple scaling formula that deals with V in the lowest-order, and Uf c up to infinite order. As Uf c becomes positive and large, however, exact numerical results deviate from lower order scaling results. In particular, the renormalized hybridization increases monotonically with increasing Uf c in contrast with the scaling theory that suggests another quantum critical point. © 2013 The Physical Society of Japan.

DOI： 10.7566/JPSJ.82.124713

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.88.024427

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To explore the nature of the metallic state near the transition to a Mott insulator, we investigate the t-J model with random exchange interaction in d=∞ dimensions. A numerically exact solution is obtained by an extension of the continuous-time quantum Monte Carlo method to the case of a vector bosonic field coupled to a local spin. We show that the paramagnetic solution near the Mott insulator describes an incoherent metal with a residual moment, and that single-particle excitations produce an additional band, which is separated from the Mott-Hubbard band. © 2013 American Physical Society.

DOI： 10.1103/PhysRevLett.110.196407

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Continuous-time quantum Monte Carlo method combined with dynamical mean field theory is used to calculate both periodic Anderson model (PAM) and Kondo lattice model (KLM). Different parameter sets of both models are connected by the Schrieffer-Wolff transformation. For degeneracy N = 2, a special particle-hole symmetric case of PAM at half filling which always fixes one electron per impurity site is compared with the results of the KLM. We find a good mapping between PAM and KLM in the limit of large on-site Hubbard interaction U for different properties like self-energy, quasiparticle residue and susceptibility. This allows us to extract quasiparticle mass renormalizations for the f electrons directly from KLM. The method is further applied to higher degenerate case and to realistic heavy fermion system CeRhIn5 in which the estimate of the Sommerfeld coefficient is proven to be close to the experimental value. DOI: 10.1103/PhysRevB.87.155106

DOI： 10.1103/PhysRevB.87.155106

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Charge order is a commonly observed phenomenon in strongly correlated materials. However, most theories are based on a repulsive intersite Coulomb interaction in order to explain charge order. Here we show that only due to local interactions, charge order is favorable in heavy fermion systems at quarter filling. The driving force is the Kondo effect, which leads to a nonlinear dependence on the filling of the lattice site for the energy gain. We use dynamical mean field theory combined with numerical renormalization group to demonstrate the existence of charge order at quarter filling for a Kondo lattice model. DOI: 10.1103/PhysRevB.87.165133

DOI： 10.1103/PhysRevB.87.165133

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Peculiar property of electronic order is clarified for the two-channel Kondo lattice. With two conduction electrons per site, the order parameter is a composite quantity involving both local and itinerant degrees of freedom. In contrast to the ordinary Kondo lattice, a heavy electron band is absent above the transition temperature, but is rapidly formed below it. The change of entropy associated with the ordering is found to be close to ln root 2 per site. This entropy corresponds to the residual entropy in a two-channel Kondo impurity, which has been regarded as due to localized free Majorana particles. The present composite order is interpreted as instability of Majorana particles toward non-Kramers conduction electrons plus heavy fermions that involve localized electrons.

DOI： 10.7566/JPSJ.82.044707

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A vector bosonic field coupled to the electronic spin is treated by means of the continuous-time quantum Monte Carlo method. In the Bose-Kondo model with a sub-Ohmic density of states ρB(ω)ωs with s=0.2, two contributions to the spin susceptibility, the Curie term T-1 and the term T-s due to bosonic fluctuations, are observed separately. This result indicates the existence of a residual moment and a hidden critical behavior. By including hybridization with itinerant electrons, a quantum critical point is identified between this local-moment state and the Kondo singlet state. It is demonstrated that the energy scale of the bosonic fluctuations is not affected by the quantum phase transition. © 2013 American Physical Society.

DOI： 10.1103/PhysRevB.87.125102

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A nonperturbative approach to unconventional superconductivity is developed based on the idea of two-particle self-consistent (TPSC) theory by Vilk and Tremblay. A sum rule, which the momentum-dependent pairing susceptibility satisfies, is derived. An effective pairing interaction between quasiparticles is determined so that the susceptibility should fulfill this exact sum rule, in which fluctuations belonging to different symmetries couple at finite momentum. It is demonstrated that the mode coupling between d- wave and s- wave pairing fluctuations leads to suppression of the d- wave fluctuation near the Mott insulator.

DOI： 10.1103/PhysRevB.85.104513

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Physics Publishing  

The Mott insulator is found in the two-channel Kondo lattice by using the dynamical mean-field theory combined with continuous-time quantum Monte Carlo method. At quarter filling of two conduction bands, the paramagnetic state shows metal-insulator crossover with increasing the coupling constant at low temperatures. The insulating state is explained by the strong coupling limit, where the system is effectively interpreted as the half-filled Hubbard model. It is shown that the present Mott insulating state is well described by the Hubbard I approximation. © Published under licence by IOP Publishing Ltd.

DOI： 10.1088/1742-6596/391/1/012155

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

A novel type of symmetry breaking is reported for the two-channel Kondo lattice where conduction electrons have spin and orbital (channel) degrees of freedom. Using the continuous-time quantum Monte Carlo and the dynamical mean-field theory, a spontaneous breaking of the orbital symmetry is observed. The tiny breakdown of orbital occupation number, however, vanishes if the conduction electrons have the particle-hole symmetry. The proper order parameter instead is identified as a composite quantity representing the orbital-selective Kondo effect. The single-particle spectrum of the selected orbital shows insulating property, while the other orbital behaves as a Fermi liquid. This composite order is the first example of odd-frequency order other than off-diagonal order (superconductivity), and is a candidate of hidden order in f-electron systems.

DOI： 10.1103/PhysRevLett.107.247202

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We show by quantum Monte Carlo simulations of realistic Kondo lattice models derived from electronic-structure calculations that multiple quantum critical points can be realized in plutonium-based materials. We place representative systems, including PuCoGa(5), on a realistic Doniach phase diagram and identify the regions where the magnetically mediated superconductivity could occur. The solution of an inverse problem to restore the quasiparticle renormalization factor for f electrons is shown to be sufficiently good to predict the trends among Sommerfeld coefficients and magnetism. A suggestion on the possible experimental verification for this scenario is given for PuAs.

DOI： 10.1103/PhysRevB.84.041105

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The impurity Green's function G(f) in the local non-Fermi liquid state is evaluated by means of the continuous-time quantum Monte Carlo method extended to the multichannel Anderson model. For N = M (where N and M are numbers of spin components and channels, respectively), G(f) is expressed as -ImG(f)(omega + i0) = c - b vertical bar omega vertical bar(1/2), and the zero-frequency value c depends only on N (= M). A corresponding impurity self-energy at low frequencies is composed of two parts: a resonance term related to c, and a non-Fermi liquid term proportional to vertical bar omega vertical bar(1/2). The characteristic energy scale is discussed in terms of the non-Fermi liquid term in the self-energy.

DOI： 10.1143/JPSJS.80SA.SA129

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This paper clarifies the microscopic nature of the staggered scalar order, which is specific to even number off electrons per site. In such systems, crystalline electric field (CEF) can make a singlet ground state. As exchange interaction with conduction electrons increases, the CEF singlet at each site gives way to Kondo singlets. The collective Kondo singlets are identified with itinerant states that form energy bands. Near the boundary of itinerant and localized states, a new type of electronic order appears with staggered Kondo and CEF singlets. We present a phenomenological three-state model that qualitatively reproduces the characteristic phase diagram, which have been obtained numerically with use of the continuous-time quantum Monte Carlo combined with the dynamical mean-field theory. The scalar order observed in PrFe4P12 is ascribed to this staggered order accompanying charge density wave (CDW) of conduction electrons. Accurate photoemission and tunneling spectroscopy should be able to probe sharp peaks both below and above the Fermi level in the ordered phase.

DOI： 10.1143/JPSJS.80SA.SA018

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

A new type of magnetism is found in the two-channel Kondo lattice where each non-Kramers doublet is coupled with two conduction bands by the orbital exchange J. The quadrupolar Kondo effect leads to an SDW state in the case of quarter filled bands, i.e., one conduction electron per site. This order is understood from the strong coupling limit with respect to J. Using the continuous-time Monte Carlo method combined with the DMFT at finite temperature T, the phase diagram is constructed in the J-T plane for the quarter filled case.

DOI： 10.1143/JPSJS.80SA.SA135

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

A microscopic model is proposed for the scalar order in PrFe4P12 where f(2) crystalline electric field (CEF) singlet and triplet states interact with two conduction bands. By combining dynamical mean-field theory and the continuous-time quantum Monte Carlo, we obtain an electronic order with staggered Kondo and CEF singlets with the total conduction number being unity per site. The ground state becomes semimetallic provided that the two conduction bands have different occupation numbers. This model naturally explains experimentally observed properties in the ordered phase of PrFe4P12 such as the scalar order parameter, temperature dependence of the resistivity, field-induced staggered moment, and inelastic features in neutron scattering. The Kondo effect plays an essential role for ordering, in strong contrast with ordinary magnetic orders by the RKKY interaction.

DOI： 10.1143/JPSJ.80.033703

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：Institute of Physics Publishing  

The generalized Kondo lattice where even number of localized electrons are coupled with two conduction bands is investigated using the dynamical mean-field theory combined with continuous-time quantum Monte Carlo method. The crystalline electric field (CEF) singlet-triplet states are taken for localized states. With one conduction electron per site, a staggered order with Kondo and CEF singlets arises. Nature of the electronic order is studied in terms of the local susceptibility. The effective CEF splitting in one sublattice remains almost the same as the original CEF splitting, while the other sublattice looks like Kondo singlets. Hence, this electronic order is interpreted as alternating sites of itinerant and localized singlet states. © Published under licence by IOP Publishing Ltd.

DOI： 10.1088/1742-6596/273/1/012034

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We present realistic Kondo-lattice simulation results for the recently discovered heavy-fermion antiferromagnet CePt(2)In(7) comparing with its three-dimensional counterpart CeIn(3) and the less two-dimensional ones, Ce-115's. We find that the distance to the magnetic quantum critical point is the largest for CeIn3 and the smallest for Ce-115's, and CePt(2)In(7) falls in between. We argue that the trend in quasi-two-dimensional materials stems from the frequency dependence of the hybridization between cerium 4f electrons and the conduction bands.

DOI： 10.1103/PhysRevB.82.180515

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The Kondo lattice model with substitutional disorder is studied with attention to the size of the Fermi surface and the associated Dingle temperature. The model serves for understanding heavy-fermion Ce compounds alloyed with La according to substitution CexLa1-x. The Fermi surface is identified from the steepest change of the momentum distribution of conduction electrons, and is derived at low enough temperature by the dynamical mean-field theory (DMFT) combined with the coherent potential approximation (CPA). The Fermi surface without magnetic field increases in size with decreasing x from x = 1 (Ce end), and disappears at such x that gives the same number of localized spins as that of conduction electrons. From the opposite limit of x = 0 (La end), the Fermi surface broadens quickly as x increases, but stays at the same position as that of the La end. With increasing magnetic field, a metamagnetic transition occurs, and the Fermi surface above the critical field changes continuously across the whole range of x. The Dingle temperature takes a maximum around x = 0.5. Implication of the results to experimental observation is discussed.

DOI： 10.1143/JPSJ.79.114709

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Novel electronic order is found theoretically for a system where even number of localized electrons per site are coupled with conduction electrons. For precise quantitative study, a variant of the Kondo lattice model is taken with crystalline electric field (CEF) singlet and triplet states for each site. Using the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method, a staggered order with alternating Kondo and CEF singlets is identified for a case with one conduction electron per site being distributed in two conduction bands each of which is quarter-filled. This electronic order accompanies a charge density wave (CDW) of conduction electrons that accumulate more on Kondo-singlet sites than on CEF-singlet sites. Possible relevance of the present order to the scalar order in PrFe4P12 is discussed.

DOI： 10.1143/JPSJ.79.074720

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DOI： 10.1103/PhysRevB.81.113108

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose a new framework for first-principles calculations of heavy-fermion materials. These are described in terms of the Kondo lattice Hamiltonian with the parameters extracted from a realistic density functional based calculation which is then solved using continuous-time quantum Monte Carlo method and dynamical mean field theory. As an example, we show our results for the Neacuteel temperatures of cerium-122 compounds (CeX(2)Si(2) with X=Ru, Rh, Pd, Cu, Ag, and Au) where the general trend around the magnetic quantum critical point is successfully reproduced. Our results are organized on a universal Doniach phase diagram in a semiquantitative way.

DOI： 10.1103/PhysRevLett.103.096403

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Physical Society of Japan  

Dynamical properties are studied numerically for a variant of the Kondo model with singlet and triplet crystalline electric field (CEF) levels where Kondo and CEF singlets compete for the ground state. Using the continuous-time quantum Monte Carlo method, we derive the $t$-matrix of conduction electrons and dynamical susceptibilities of local electrons without encountering the negative sign problem. When the CEF splitting is comparable to the Kondo temperature, the dynamical response has only a quasi-elastic peak. Nevertheless, the local single-particle spectrum shows an energy gap in strong contrast with the ordinary Kondo model.

DOI： 10.1143/JPSJ.78.074719

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Magnetic and charge susceptibilities in the Kondo lattice are derived by the continuous-time quantum Monte Carlo (CT-QMC) method combined with the dynamical mean-field theory. For a weak exchange coupling J and near half filling of the conduction band, antiferromagnetic transition occurs as signalled by divergence of the staggered magnetic susceptibility with lowering temperature. With increasing J, the Kondo effect Suppresses the divergence, and the critical value of J agrees well with Doniach's estimate which considers the RKKY interaction as competing with the Kondo effect. For low density of conduction electrons, a ferromagnetic ordering is observed where Doniach's estimate does not work. Around quarter tilling, a charge-density-wave (CDW) transition is found. The CDW is interpreted from the strong-coupling limit in terms of effective repulsion between Kondo singlets.

DOI： 10.1143/JPSJ.78.034719

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：The Physical Society of Japan (JPS)  

A Green-function formalism for the Kondo lattice model is presented, which is designed to be combined with dynamical mean-field theory. Using Wick's theorem only for conduction electrons, dynamical quantities are represented in terms of the $t$-matrix and its two-particle generalizations. By taking the high-frequency limit of the $t$-matrix with respect to a part of the fermion frequencies, one obtains dynamical correlation functions of localized moments. Explicit examples of calculation steps are provided using the continuous-time quantum Monte Carlo method.

DOI： 10.1143/JPSJ.78.014702

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

PrFe4P12 exhibits clear heavy electron behaviors as well as the phase transition to an antiferro-type ordering of 4f electron state. In this paper, we report on inelastic neutron scattering results for powdered samples of PrxLa1-xFe4P12 (x = 1.00 and 0.85). A clear quasielastic magnetic response is observed, and no distinct signal is seen for crystal-field (CF) excitations in the heavy electron state. A model with strong hybridization between conduction electrons and Pr3+ 4f(2) electrons [J. Otsuki et al.: J. Phys. Soc. Jpn. 74 (2005) 200 and 2082] is consistent with the observed magnetic response. This result shows that the heavy electron behavior of PrxLa1-xFe4P12 (x = 1.00 and 0.85) originates from the Kondo effect associated with low-lying singlet-triplet CF states.

DOI： 10.1143/JPSJ.77.063706

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

An impurity solver based on a continuous-time quantum Monte Carlo method is developed for the Coqblin-Schrieffer model. The Monte Carlo simulation does not encounter a sign problem for antiferromagnetic interactions, and accurately reproduces the Kondo effect. Our algorithm can deal with an arbitrary number N of local degrees of freedom, becomes more efficient for larger values of N, and is hence suitable for models with orbital degeneracy. The dynamical susceptibility and the impurity t-matrix are derived with the aid of the Pade approximation for various values of N, and good agreement is found with other methods and available exact results. We point out that the Korringa-Shiba relation needs correction for a finite value of the exchange interaction.

DOI： 10.1143/JPSJ.76.114707

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

The Anderson model with the Coulomb interaction between the local and conduction electrons is studied in the semiconducting phase. Based on a perturbation theory from the atomic limit, leading contributions for the c-f Coulomb interaction are incorporated as a vertex correction to hybridization. An analytical solution shows that the effective attraction in the intermediate states leads to a bound state localized at the local electron site. Self-consistent equations are constructed as an extension of the non-crossing approximation (NCA) to include the vertex part yielding the bound state. A numerical calculation demonstrates the excitonic bound state inside the semiconducting gap for single-particle excitations, and a discontinuity at the gap edge for magnetic excitations.

DOI： 10.1143/JPSJ.76.064707

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

The effective mass probed by the de Haas-van Alphen oscillations is studied for a model Ce system under magnetic field higher than the Kondo energy. In the mean-field theory, the mass enhancement per Ce ion in the periodic system is identical with that in the dilute system. With decreasing magnetic field, the effective mass tends to diverge corresponding to a formation of the Kondo ground state. The effective mass can be very different between up and down spins depending on the nature of the 4f wave functions. (c) 2006 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jmmm.2006.10.265

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

The non-crossing approximation (NCA) is generalized for the Anderson model with finite Coulomb repulsion U. Resummation of infinite number of terms is performed so as to incorporate all leading contributions in the limit of large degeneracy of the local states. With negligible weight of the doubly occupied local states in equilibrium, the extension is achieved through simple modifications of the lowest order formulae. The single-particle excitation spectrum is calculated with almost the same computational effort as in the original NCA. The present scheme reproduces the scaling behavior of the Kondo resonance in the density of states, and gives reasonable description of thermodynamics of the finite-U Anderson model over a wide range of temperature.

DOI： 10.1143/JPSJ.75.064707

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Characteristics of hybridization and multipole orders of 4f-electrons in Pr skutterudites are explained in terms of a pseudo-quartet composed of crystalline electric field (CET) singlet and the triplet. It is shown that the contrasting behaviors observed in PrFe4P12 and PrOs4Sb12 are ascribed to the difference in triplet Wave functions and the CEF splittings. Since a macroscopic degeneracy remains even in the ordered phase with the F-3-type antiferro-quadrupole (AFQ) order, a model with strong AFQ fluctuation and static monopole/hexadecapole order is proposed for PrFe4 P12 The remaining cubic symmetry explains qualitatively the behavior of staggered magnetization observed by NMR and neutron scattering. For identification of possible hexadecapole orders in PrFe4P12, and PrRu4P12, eightfold intensity pattern is predicted in the azimuthal angle scan of resonant X-ray scattering. In PrOs4Sb12, the ferromagnetic exchange coupling with the conduction band does not lead to magnetic Kondo effect, but a momentum-dependent quadrupole coupling can give rise to enhanced effective mass, is should be sensitive to disorder.

DOI： 10.1143/JPSJS.75S.209

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Language：English   Publishing type：Research paper (scientific journal)  

Dynamics of the singlet-triplet crystalline electric field (CEF) system at finite temperatures is discussed by use of the non-crossing approximation. Even though the Kondo temperature is smaller than the excitation energy to the CEF triplet, the Kondo effect appears at temperatures higher than the CEF splitting, and accordingly only quasi-elastic peak is found in the magnetic spectra. On the other hand, at lower temperatures the CEF splitting suppresses the Kondo effect and inelastic peak develops. The broad quasi-elastic neutron scattering spectra observed in PrFe4P12 at temperatures higher than the quadrupole order correspond to the parameter range where the CEF splittings are unimportant. ©2005 The Physical Society of Japan.

DOI： 10.1143/JPSJ.74.2082

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Language：English   Publishing type：Research paper (scientific journal)  

Possible Kondo effect in Pr skutterudite is studied with attention to characteristic features of low-lying crystalline electric field (CEF) levels and the conduction band. A mechanism for the small CEF splitting between a singlet and a triplet is proposed as combination of the point-charge interaction and hybridization of 4f with ligand p states. Provided 4f 3 configurations dominate over 4f 1 as intermediate states, p-f hybridization favors the triplet, while point-charge interaction favors the singlet. For realistic parameters for hybridization as well as 4f 1 and 4f 3 levels, these singlet and triplet can form a nearly degenerate pseudo-quartet. It is found that one of two spin 1/2 objects composing the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The magnitude of each effective exchange depends strongly on a parameter characterizing the triplet wave function under the T h symmetry. It is argued that differences of this parameter among Pr skutterdudites are responsible for the apparent diversity of their physical properties. Numerical renormalization group is used to derive the renormalization flows going toward singlet, doublet, triplet or quaret according to the CEF splitting and exchange interactions. ©2005 The Physical Society of Japan.

DOI： 10.1143/JPSJ.74.200

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Language：Japanese  

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DOI： 10.1016/j.physb.2006.01.092

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Language：English   Publisher：PHYSICAL SOC JAPAN  

Integral equations for thermodynamic quantities are derived in the framework of the non-crossing approximation (NCA). Entropy and specific heat of 4f contribution are calculated without numerical differentiations of thermodynamic potential. The formulation is applied to systems such as PrFe4P12 with singlet-triplet crystalline electric field (CEF) levels.

DOI： 10.1143/JPSJS.75S.256

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Language：English  

Theoretical account is given of 4f-electron dynamics and multipole orders in Pr skutterudites with particular attention to (i) mechanism of the crystalline electric field (CEF) splitting leading to a pseudo-quartet ground state
(ii) Kondo effect due to exchange interactions involving the pseudo-quartet
(iii) multipole orders in the lattice of the pseudo-quartet in magnetic field. Competition between the point-charge interaction and hybridization between 4f and conduction electrons is identified as the key for controlling the CEF splitting. It is found that one of two pseudo-spins forming the pseudo-quartet has a ferromagnetic exchange, while the other has an antiferromagnetic exchange with conduction electrons. The Kondo effect is clearly seen in the resistivity calculated by the NCA, provided the low-lying triplet above the singlet is mainly composed of the Γ4-type wave functions. If the weight of the Γ5-type is large in the triplet, the Kondo effect does not appear. This difference caused by the nature of the triplet explains the presence of the Kondo effect in PrFe4P12, and its absence in PrOs4Sb12. By taking the minimal model with antiferro-quadrupole (AFQ) and ferro-type intersite interactions for dipoles and octupoles between nearest-neighbors, the mean-field theory reproduces the overall feature of the multiple ordered phases in PrFe4P12. The AFQ order with the Γ3-type symmetry is found to be stable only as a mixture of O2 0 and O2 2 components.

DOI： 10.1143/PTPS.160.134

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