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

physica status solidi (b)

Thermodynamic properties of uniform and dimerized hubbard chains

B. Lorenz

Published Oct 1, 1983• 7 citations
Publisher

Abstract

Abstract The thermodynamics of the uniform and dimerized half‐filled Hubbard chains is investigated within an approximation which takes into account the correlations in a given cluster of sites and which is valid for all model parameters and for all temperatures. The dependence of the specific heat on temperature changes from a one‐peak to a two‐peak structure with increasing interaction strength. The influence of dimerization is discussed. The local magnetic moment is found to decrease with increasing temperature in the high‐temperature region. It is suggested that this qualitative behaviour is more general and independent on dimension and band filling.

DOI
10.1002/pssb.2221190215

Related papers

Thermodynamic and correlation functions of half-filled-band Hubbard dimer, dimerized, and uniform Hubbard chains

Charles C. Chen

The thermodynamic and two-site correlation functions for the half-filled-band isolated Hubbard dimer, dimerized, and uniform Hubbard chains for different values of the Coulomb energy $U$ are evaluated in a unified way in the pair approximation of the cluster-variation method. The energy, specific heat, and correlation functions as functions of temperature for different ratios of $\frac{{t}^{\ensuremath{'}}}{t}$ ($t$, ${t}^{\ensuremath{'}}$ are intradimer and interdimer transfer integrals, respectively) and $\frac{U}{t}$ are obtained. Our solutions for the Hubbard dimer are exact and agree with those obtained from the partition function. Solutions for the dimerized and uniform Hubbard chains correspond to the Bethe approximations in which all two-site correlations are taken into account. It is observed that the chemical potential for the half-filled dimerized Hubbard Hamiltonian is exactly $\frac{U}{2}$ at all temperatures, independent of the transfer integrals $t$ or ${t}^{\ensuremath{'}}$.

Physical review. B, Solid state•Aug 15, 1977•7 citations

Thermodynamic properties of the dimerized half-filled-band Hubbard chain

U. Bernstein, Philip A. Pincus

The dimerized-chain Hubbard model is characterized by a Coulomb energy $U$ and two alternating transfer constants, an intradimer constant $t$, and a smaller interdimer constant ${t}^{\ensuremath{'}}$. We have used thermodynamic perturbation theory to treat the half-filled-band case, taking the interdimer transfer as the perturbation term. The unperturbed problem is a lattice of isolated dimers. We give the energy, specific heat, and magnetic susceptibility as functions of temperature for the unperturbed case and for the first nonvanishing order in the perturbation. The results are consistent with the $U=0$ case, which is solved exactly. The interdimer transfer ${t}^{\ensuremath{'}}$ has the effect of distorting the peaks in the specific heat and reducing the susceptibility; this is shown graphically.

Physical review. B, Solid state•Oct 15, 1974•17 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

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

Thermodynamic properties of one-dimensional hubbard model at finite temperatures

Yang C; Kocharian AN; Chiang YL

[[abstract]]The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.

•Jan 1, 2003•0 citations

Thermodynamic properties of one-dimensional Hubbard model at finite temperatures

Chia‐Wei Yang

The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0<q<π) into the state with strong antiferromagnetic correlations (q=π) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.

•Aug 10, 2003•1 citation
Abstract The thermodynamics of the uniform and dimerized half‐filled Hubbard chains is investigated within an approximation which takes into account the correlations in a given cluster of sites and which is valid for all model parameters and for all temperatures. The dependence of the specific heat on temperature changes from a one‐peak to a two‐peak structure with increasing interaction strength. The influence of dimerization is discussed. The local magnetic moment is found to decrease with increasing temperature in the high‐temperature region. It is suggested that this qualitative behaviour is more general and independent on dimension and band filling.
The thermodynamic and two-site correlation functions for the half-filled-band isolated Hubbard dimer, dimerized, and uniform Hubbard chains for different values of the Coulomb energy UUU are evaluated in a unified way in the pair approximation of the cluster-variation method. The energy, specific heat, and correlation functions as functions of temperature for different ratios of $\frac{{t}^{\ensuremath{'}}}{t}$ (ttt, ${t}^{\ensuremath{'}}$ are intradimer and interdimer transfer integrals, respectively) and Ut\frac{U}{t}tU​ are obtained. Our solutions for the Hubbard dimer are exact and agree with those obtained from the partition function. Solutions for the dimerized and uniform Hubbard chains correspond to the Bethe approximations in which all two-site correlations are taken into account. It is observed that the chemical potential for the half-filled dimerized Hubbard Hamiltonian is exactly U2\frac{U}{2}2U​ at all temperatures, independent of the transfer integrals ttt or ${t}^{\ensuremath{'}}$.
The dimerized-chain Hubbard model is characterized by a Coulomb energy UUU and two alternating transfer constants, an intradimer constant ttt, and a smaller interdimer constant ${t}^{\ensuremath{'}}$. We have used thermodynamic perturbation theory to treat the half-filled-band case, taking the interdimer transfer as the perturbation term. The unperturbed problem is a lattice of isolated dimers. We give the energy, specific heat, and magnetic susceptibility as functions of temperature for the unperturbed case and for the first nonvanishing order in the perturbation. The results are consistent with the U=0U=0U=0 case, which is solved exactly. The interdimer transfer ${t}^{\ensuremath{'}}$ has the effect of distorting the peaks in the specific heat and reducing the susceptibility; this is shown graphically.
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.
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.
[[abstract]]The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0<q<π) into the state with strong antiferromagnetic correlations (q=π) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.