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

arXiv:cond-mat/9401017 · Physical review. B, Condensed matter

Partition functional and thermodynamic properties of the infinite-dimensional Hubbard model

Y. M. Li, N. d’Ambrumenil

Published Mar 1, 1994• 4 citations
arXivHTMLPDF

Abstract

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature ${\mathit{T}}^{\mathrm{*}}$. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near ${\mathit{T}}^{\mathrm{*}}$. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around ${\mathit{T}}^{\mathrm{*}}$, and has a rough linear temperature dependence above ${\mathit{T}}^{\mathrm{*}}$.

DOI
10.1103/physrevb.49.6058

Related papers

PARTITION FUNCTIONAL AND THERMODYNAMIC PROPERTIES OF THE INFINITE-DIMENSIONAL HUBBARD-MODEL

No author provided

An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature T*. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near T*. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around T*, and has a rough linear temperature dependence above T*.

•Sep 10, 2026•0 citations

A SELF-ENERGY FUNCTIONAL FOR THE INFINITE-DIMENSIONAL HUBBARD MODEL

Y.M. Li, N. d’Ambrumenil

We present an approximate self-energy functional for the infinite-dimensional Hubbard model. This functional is a natural extension of the exact solution of the Falicov-Kimball model to the spin-symmetric case, and is exact in the uncorrelated and atomic limits. Using the functional we calculate the susceptibility and the specific heat for the Lorentzian density of states. We find that the susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations to a Fermi liquid state at low temperature via a Kondo-type anomaly. The specific heat shows a peak at the corresponding Kondo temperature.

Modern Physics Letters B•Dec 10, 1992•7 citations

Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model

Hiroyuki Shiba, Philip A. Pincus

In order to investigate the thermal properties (specific heat, magnetic susceptibility, entropy, internal energy, and some correlation functions) of the one-dimensional half-filled-band Hubbard model, we have studied linear chains and rings containing two to six atoms, by performing machine calculations. Supplementing the low-temperature behavior obtained from the exact solution for the infinite chain by Lieb and Wu, our results should be suggestive of the properties of the infinite system throughout the entire temperature domain. It is shown that when the ratio of the correlation energy $U$ to the total width $\ensuremath{\Delta}$ of the band of single-particle excitations is larger than 1, the specific heat has two peaks. The high-temperature peak arises from the gradual metal-insulator transition (or the gradual formation of local moments), while the low-temperature peak is associated with the antiferromagnetic short-range ordering. When $\frac{U}{\ensuremath{\Delta}}$ becomes small, the two peaks merge into one. This picture is consistent with all other thermal properties, including correlation functions. The high-temperature properties are compared with the results predicted by Hubbard's approximate theory based on the truncation of the equations of motion of the Green's functions.

Physical review. B, Solid state•Mar 1, 1972•201 citations

One-dimensional extended Hubbard model in the atomic limit

Francesco Paolo Mancini, Francesco Paolo Mancini

We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.

arXiv:0804.4419•Physical Review E•Jun 16, 2008•41 citations

Thermodynamic Properties of the One-Dimensional Half-Filled-Band Hubbard Model. II

Hiroyuki Shiba

In order to determine finite-temperature properties of the infinite one-dimensional Hubbard model for the half-filled band, finite systems such as chains with 2 to 5 atoms and rings with 4 and 6 atoms are studied with the application of the grand canonical ensemble. The obtained temperature dependence of the specific heat, the entropy, the magnetic susceptibility and some correlation functions clearly shows a rearrangement of the electronic state of the system with the increase of the strength of the Coulomb interaction relative to the transfer integral. In the light of our new results the functional integral approach recently proposed by Kimball and Schrieffer as well as Hubbard's approximate theory is examined.

Progress of Theoretical Physics•Dec 1, 1972•280 citations

Thermodynamics of the one-dimensional half-filled-band Falicov-Kimball model

Cláudio Andrade Macedo, L. G. Azevedo, André M. C. Souza

In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.

Physical review. B, Condensed matter•Oct 25, 2001•20 citations
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature T∗{\mathit{T}}^{\mathrm{*}}T∗. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near T∗{\mathit{T}}^{\mathrm{*}}T∗. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around T∗{\mathit{T}}^{\mathrm{*}}T∗, and has a rough linear temperature dependence above T∗{\mathit{T}}^{\mathrm{*}}T∗.
An approximate partition functional is derived for the infinite-dimensional Hubbard model. This functional naturally includes the exact solution of the Falicov-Kimball model as a special case, and is exact in the uncorrelated and atomic limits. It explicitly keeps spin symmetry. For the case of the Lorentzian density of states, we find that the Luttinger theorem is satisfied at zero temperature. The susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations at high temperature to a correlated state at low temperature via a Kondo-type anomaly at a characteristic temperature T*. We attribute this anomaly to the appearance of the Hubbard pseudogap. The specific heat also shows a peak near T*. The resistivity goes to zero at zero temperature, in contrast to other approximations, rises sharply around T*, and has a rough linear temperature dependence above T*.
We present an approximate self-energy functional for the infinite-dimensional Hubbard model. This functional is a natural extension of the exact solution of the Falicov-Kimball model to the spin-symmetric case, and is exact in the uncorrelated and atomic limits. Using the functional we calculate the susceptibility and the specific heat for the Lorentzian density of states. We find that the susceptibility crosses over smoothly from that expected for an uncorrelated state with antiferromagnetic fluctuations to a Fermi liquid state at low temperature via a Kondo-type anomaly. The specific heat shows a peak at the corresponding Kondo temperature.
In order to investigate the thermal properties (specific heat, magnetic susceptibility, entropy, internal energy, and some correlation functions) of the one-dimensional half-filled-band Hubbard model, we have studied linear chains and rings containing two to six atoms, by performing machine calculations. Supplementing the low-temperature behavior obtained from the exact solution for the infinite chain by Lieb and Wu, our results should be suggestive of the properties of the infinite system throughout the entire temperature domain. It is shown that when the ratio of the correlation energy UUU to the total width $\ensuremath{\Delta}$ of the band of single-particle excitations is larger than 1, the specific heat has two peaks. The high-temperature peak arises from the gradual metal-insulator transition (or the gradual formation of local moments), while the low-temperature peak is associated with the antiferromagnetic short-range ordering. When $\frac{U}{\ensuremath{\Delta}}$ becomes small, the two peaks merge into one. This picture is consistent with all other thermal properties, including correlation functions. The high-temperature properties are compared with the results predicted by Hubbard's approximate theory based on the truncation of the equations of motion of the Green's functions.
We present the exact solution of the one-dimensional extended Hubbard model in the atomic limit within the Green's function and equations of motion formalism. We provide a comprehensive and systematic analysis of the model by considering all the relevant response and correlation functions as well as thermodynamic quantities in the whole parameters space. At zero temperature we identify four phases in the plane (U,n) ( U is the on-site potential and n is the filling) and relative phase transitions as well as different types of charge ordering. These features are endorsed by investigating at T=0 the chemical potential and pertinent local correlators, the particle and double occupancy correlation functions, the entropy, and by studying the behavior in the limit T-->0 of the charge and spin susceptibilities. A detailed study of the thermodynamic quantities is also presented at finite temperature. This study evidences that a finite-range order persists for a wide range of the temperature, as shown by the behavior of the correlation functions and by the two-peak structure exhibited by the charge susceptibility and by the entropy. Moreover, the equations of motion formalism, together with the use of composite operators, allows us to exactly determine the set of elementary excitations. As a result, the density of states can be determined and a detailed analysis of the specific heat allows for identifying the excitations and for ascribing its two-peak structure to a redistribution of the charge density.
In order to determine finite-temperature properties of the infinite one-dimensional Hubbard model for the half-filled band, finite systems such as chains with 2 to 5 atoms and rings with 4 and 6 atoms are studied with the application of the grand canonical ensemble. The obtained temperature dependence of the specific heat, the entropy, the magnetic susceptibility and some correlation functions clearly shows a rearrangement of the electronic state of the system with the increase of the strength of the Coulomb interaction relative to the transfer integral. In the light of our new results the functional integral approach recently proposed by Kimball and Schrieffer as well as Hubbard's approximate theory is examined.
In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.