Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Local approximation to the spinless Falicov-Kimball model

James K. Freericks

Published Nov 15, 1993• 14 citations
Publisher

Abstract

The local approximation is applied to the spinless Falicov-Kimball model in one and two dimensions. The local approximation may be viewed as a zeroth-order expansion in 1/d that is exact in the weak-coupling limit. The local approximation rapidly becomes inaccurate as a function of interaction strength in one dimension, but is accurate in two dimensions. This result indicates that the 1/d expansion converges rapidly for the Falicov-Kimball model in d\ensuremath{\ge}2 and that exact solutions of many-body problems in infinite dimensions are quantitatively relevant for physical dimensions.

DOI
10.1103/physrevb.48.14797

Related papers

Non-local effects in the fermion dynamical mean-field framework; application to the two-dimensional Falicov-Kimball model

M. S. Laad, Mathias van den Bossche

We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D = solution. In contrast to the usual D = case, the self-energy is self-consistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large- D solution, and allows one to undertake a systematic study of the effects of inclusion of k -dependent effects on the D = picture. Results for the density of states ( ), and the single-particle spectral density for the 2D Falicov-Kimball model always yield positive definite ( ), and the spectral function shows striking new features inaccessible for D = . Our results are in good agreement with the exact results known from the 2D Falicov-Kimball model.

Journal of Physics Condensed Matter•Feb 24, 2000•3 citations

Systematic 1/d Corrections to the Infinite-Dimensional Limit of Correlated Lattice Electron Models

Avraham Schiller, Kevin Ingersent

We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions $d$. This involves a systematic expansion in powers of $1/d$ about the limit $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$.

Physical Review Letters•Jul 3, 1995•71 citations

Two-state one-dimensional spinless Fermi gas

James K. Freericks, L. M. Falicov

The two-state, one-dimensional, spinless Fermi gas (Falicov-Kimball model) is studied exactly by numerical calculation and perturbation theory. Rigorous results are presented for small interaction strength and (restricted) coherent and incoherent phase diagrams are calculated for two specific examples. The numerical calculations are extrapolated to provide a qualitative picture of the complete solution. The result includes a fractal structure in which the ground-state changes discontinuously as a function of the parameters.

Physical review. B, Condensed matter•Feb 1, 1990•80 citations

Non-local effects in the fermion Dynamical mean field framework. Application to the 2D Falicov-Kimball model

M. S. Laad, Mathias van den Bossche

We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the $D=\infty$ solution. In contrast to usual $D=\infty$, the selfenergy is selfconsistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large-D solution, and allows one to undertake a systematic study of the effects of inclusion of k-dependent effects on the $D=\infty$ picture. Results for the density of states $ρ(ω)$, and the single particle spectral density for the 2D Falicov-Kimball model always yield positive definite $ρ(ω)$, and the spectral function shows striking new features inaccessible in $D=\infty$. Our results are in good agreement with the exact results known on the 2D Falikov-Kimball model.

arXiv:cond-mat/9802176•Feb 17, 1998•0 citations

Exact dynamical mean-field theory of the Falicov-Kimball model

James K. Freericks, V. Zlatić

The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions, which provides an interesting benchmark for the physics of locally correlated systems. In this review, the authors develop the formalism for solving the Falicov-Kimball model from a path-integral perspective and provide a number of expressions for single- and two-particle properties. Many important theoretical results are examined that show the absence of Fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge-density-wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including ${\mathrm{YbInCu}}_{4},$ ${\mathrm{EuNi}}_{2}({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}{)}_{2},$ ${\mathrm{NiI}}_{2},$ and ${\mathrm{Ta}}_{x}\mathrm{N}].$

arXiv:cond-mat/0301188•Reviews of Modern Physics•Oct 30, 2003•350 citations

Bosonization Solution of the Falicov-Kimball Model

P. M. R. Brydon, M. Gulácsi

We use a novel approach to analyze the one-dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states: We find a crossover between the well-known weak- and strong-coupling behaviors. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.

arXiv:cond-mat/0506218•Physical Review Letters•Jan 25, 2006•5 citations
The local approximation is applied to the spinless Falicov-Kimball model in one and two dimensions. The local approximation may be viewed as a zeroth-order expansion in 1/d that is exact in the weak-coupling limit. The local approximation rapidly becomes inaccurate as a function of interaction strength in one dimension, but is accurate in two dimensions. This result indicates that the 1/d expansion converges rapidly for the Falicov-Kimball model in d\ensuremath{\ge}2 and that exact solutions of many-body problems in infinite dimensions are quantitatively relevant for physical dimensions.
We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D = solution. In contrast to the usual D = case, the self-energy is self-consistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large- D solution, and allows one to undertake a systematic study of the effects of inclusion of k -dependent effects on the D = picture. Results for the density of states ( ), and the single-particle spectral density for the 2D Falicov-Kimball model always yield positive definite ( ), and the spectral function shows striking new features inaccessible for D = . Our results are in good agreement with the exact results known from the 2D Falicov-Kimball model.
We present a self-consistent treatment of Hubbard-like lattice models at large, but finite, spatial dimensions ddd. This involves a systematic expansion in powers of 1/d1/d1/d about the limit $d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$. The first-order corrections can be obtained by self-consistent solution of coupled one- and two-impurity models. We calculate the leading corrections to properties of the Falicov-Kimball model. The infinite-dimensional limit seems to describe this particular model remarkably well even for d=2d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2d=2.
The two-state, one-dimensional, spinless Fermi gas (Falicov-Kimball model) is studied exactly by numerical calculation and perturbation theory. Rigorous results are presented for small interaction strength and (restricted) coherent and incoherent phase diagrams are calculated for two specific examples. The numerical calculations are extrapolated to provide a qualitative picture of the complete solution. The result includes a fractal structure in which the ground-state changes discontinuously as a function of the parameters.
We propose a new, controlled approximation scheme that explicitly includes the effects of non-local correlations on the D=∞D=\inftyD=∞ solution. In contrast to usual D=∞D=\inftyD=∞, the selfenergy is selfconsistently coupled to two-particle correlation functions. The formalism is general, and is applied to the two-dimensional Falicov-Kimball model. Our approach possesses all the strengths of the large-D solution, and allows one to undertake a systematic study of the effects of inclusion of k-dependent effects on the D=∞D=\inftyD=∞ picture. Results for the density of states ρ(ω)ρ(ω)ρ(ω), and the single particle spectral density for the 2D Falicov-Kimball model always yield positive definite ρ(ω)ρ(ω)ρ(ω), and the spectral function shows striking new features inaccessible in D=∞D=\inftyD=∞. Our results are in good agreement with the exact results known on the 2D Falikov-Kimball model.
The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions, which provides an interesting benchmark for the physics of locally correlated systems. In this review, the authors develop the formalism for solving the Falicov-Kimball model from a path-integral perspective and provide a number of expressions for single- and two-particle properties. Many important theoretical results are examined that show the absence of Fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge-density-wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu4,{\mathrm{YbInCu}}_{4},YbInCu4​, ${\mathrm{EuNi}}_{2}({\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}{)}_{2},$ NiI2,{\mathrm{NiI}}_{2},NiI2​, and TaxN].{\mathrm{Ta}}_{x}\mathrm{N}].Tax​N].
We use a novel approach to analyze the one-dimensional spinless Falicov-Kimball model. We derive a simple effective model for the occupation of the localized orbitals which clearly reveals the origin of the known ordering. Our study is extended to a quantum model with hybridization between the localized and itinerant states: We find a crossover between the well-known weak- and strong-coupling behaviors. The existence of electronic polarons at intermediate coupling is confirmed. A phase diagram is presented and discussed in detail.