We study the antiferromagnetic and paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half filling using the cellular dynamical mean-field theory (CDMFT) with the numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the nonlocal correlations increase the gap in both the antiferromagnetic and Kondo insulator phases and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.
We study the antiferromagnetic and paramagnetic Kondo insulator phases of the Kondo lattice model on the cubic lattice at half filling using the cellular dynamical mean-field theory (CDMFT) with the numerical renormalization group (NRG) as the impurity solver, focusing on the fine details of the spectral function and self-energy. We find that the nonlocal correlations increase the gap in both the antiferromagnetic and Kondo insulator phases and shrink the extent of the antiferromagnetic phase in the phase diagram but do not alter any properties qualitatively. The agreement between the numerical CDMFT results and those within a simple hybridization picture, which adequately describes the overall band structure of the system but neglects all effects on the inelastic-scattering processes, is similar to that of the single-site DMFT results; there are deviations that are responsible for the additional fine structure, in particular for the asymmetric spectral resonances or dips that become more pronounced in the strong-coupling regime close to the antiferromagnet-paramagnetic quantum phase transition. These features appear broader in the CDMFT mostly due to numerical artifacts linked to more aggressive state truncation required in the NRG.
We study paramagnetic quantum criticality in the periodic Anderson model (PAM) using cellular dynamical mean-field theory (CDMFT), with the numerical renormalization group (NRG) as a cluster impurity solver. The PAM describes itinerant c electrons hybridizing with a lattice of localized f electrons. At zero temperature, it exhibits a much-studied quantum phase transition from a Kondo phase to a Ruderman-Kittel-Kasuya-Yosida (RKKY) phase when the hybridization is decreased through a so-called Kondo breakdown quantum critical point (KB QCP). There, Kondo screening of f spins by c electrons breaks down, so that f excitations change their character from somewhat itinerant to mainly localized, while c excitations remain itinerant. Building on , which interpreted the KB transition as an orbital-selective Mott transition, we here elucidate its nature in great detail by performing a high-resolution, real-frequency study of various dynamical quantities (susceptibilities, self-energies, and spectral functions). NRG allows us to study the quantum critical regime governed by the QCP and located between two temperature scales, T FL < T NFL . In this regime, we find fingerprints of non-Fermi-liquid (NFL) behavior in several dynamical susceptibilities. Surprisingly, CDMFT self-consistency is essential to stabilize the QCP and the NFL regime. The Fermi-liquid (FL) scale T FL decreases toward and vanishes at the KB QCP; at temperatures below T FL , FL behavior emerges. At T = 0 , we find the following properties. The KB transition is continuous. The f quasiparticle weight decreases continuously as the transition is approached from either side, vanishing only at the KB QCP. Therefore, the quasiparticle weight of the f band is nonzero not only in the Kondo phase, but also in the RKKY phase; hence, the FL quasiparticles comprise c f electrons in both phases. The Fermi surface (FS) volumes in the two phases differ, implying a FS reconstruction at the KB QCP. Whereas the large-FS Kondo phase has a two-band structure as expected, the small-FS RKKY phase unexpectedly has a three-band structure. We provide a detailed analysis of quasiparticle properties of both the Kondo and, for the first time, also the RKKY phase and uncover their differences. The FS reconstruction is accompanied by the appearance of a Luttinger surface on which the f self-energy diverges. The volumes of the Luttinger and Fermi surfaces are related to the charge density by a generalized Luttinger sum rule. We interpret the small FS volume and the emergent Luttinger surface as evidence for f -electron fractionalization in the RKKY phase. Finally, we compute the temperature dependence of the Hall coefficient and the specific heat, finding good qualitative agreement with experiments. Published by the American Physical Society 2024
Using a cluster extension of the dynamical mean-field theory (CDMFT) we map out the magnetic phase diagram of the anisotropic square lattice Hubbard model with nearest-neighbor intrachain t and interchain ${t}_{\ensuremath{\perp}}$ hopping amplitudes at half filling. A fixed value of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}=\ensuremath{-}{t}_{\ensuremath{\perp}}/2$ removes the nesting property of the Fermi surface and stabilizes a paramagnetic metal phase in the weak-coupling regime. In the isotropic and moderately anisotropic regions, a growing spin entropy in the metal phase is quenched out at a critical interaction strength by the onset of long-range antiferromagnetic (AF) order of preformed local moments. It gives rise to a first-order metal-insulator transition consistent with the Mott-Heisenberg picture. In contrast, a strongly anisotropic regime ${t}_{\ensuremath{\perp}}/t\ensuremath{\lesssim}0.3$ displays a quantum critical behavior related to the continuous transition between an AF metal phase and the AF insulator. Hence, within the present framework of CDMFT, the opening of the charge gap is magnetically driven as advocated in the Slater picture. We also discuss how the lattice-anisotropy-induced evolution of the electronic structure on a metallic side of the phase diagram is tied to the emergence of quantum criticality.
Abstract We formulate a quantum embedding algorithm in real-space for the simultaneous theoretical treatment of nonlocal electronic correlations and disorder, the coherent cellular dynamical mean-field theory (C-CDMFT). This algorithm combines the molecular coherent potential approximation (CPA) with the cellular dynamical mean-field theory. After a pedagogical review of quantum embedding theories for disordered and interacting electron systems, and a detailed discussion of its work flow, we present first results from C-CDMFT for the half-filled two-dimensional Anderson–Hubbard model on a square lattice: (i) the analysis of its Mott metal–insulator transition as a function of disorder strength, and (ii) the impact of different types of disorder on its magnetic phase diagram. For the latter, by means of a ‘disorder diagnostics’, we are able to precisely identify the contributions of different disorder configurations to the system’s magnetic response.
We study the Hubbard model at half band-filling on a Bethe lattice with infinite coordination number in the paramagnetic insulating phase at zero temperature. We use the dynamical mean-field theory (DMFT) mapping to a single-impurity Anderson model with a bath whose properties have to be determined self-consistently. For a controlled and systematic implementation of the self-consistency scheme we use the fixed-energy (FE) approach to the DMFT. In FE-DMFT the onset and the width of the Hubbard bands are adjusted self-consistently but the energies of the bath levels are kept fixed relatively to both band edges during the calculation of self-consistent hybridization strengths between impurity and bath sites. Using the dynamical density-matrix renormalization group method (DDMRG) we calculate the density of states with a resolution ranging from 3% of the bare bandwidth W=4t at high energies to 0.5% in the vicinity of the gap. The DDMRG resolution and accuracy for the density of states and the gap is superior to those obtained with other numerical methods in previous DMFT investigations. We find that the Mott gap closes at a critical coupling Uc/t=4.45±0.05. At U=4.5t, we observe prominent shoulders near the onset of the Hubbard bands. They are the remainders of the quasi-particle resonance in the metallic phase which appears to split when the gap opens at Uc.
Heavy-fermion or Kondo lattice materials are considered to be typical strongly correlated systems, for which mean-field approximations have shown that the Coulomb interaction increases the effective mass and narrows the band gap. In this paper, to clarify interaction effects on the electronic excitation, the spectral function of the Kondo lattice and periodic Anderson models is studied around Kondo insulators in the strong-coupling regime, by using the non-Abelian dynamical density-matrix renormalization group method and perturbation theory. Upon doping a Kondo insulator, an electronic mode emerges in the Kondo insulating gap, exhibiting the momentum-shifted magnetic dispersion relation. Although the ground-state properties are similar to those of a doped band insulator, the emergence of the electronic mode reflecting spin-charge separation of the Kondo insulator is a crucial interaction effect that allows us to regard the Kondo-insulator--metal transition as a type of Mott transition. In addition, electronic modes emerge even in the high-energy regime by doping in the periodic Anderson model. These strong-correlation effects have not been expected in conventional mean-field approximations and would bring a different perspective on heavy-fermion or Kondo lattice systems.
In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal–insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a combination of the cellular dynamical mean-field theory (CDMFT) and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.