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

Strong-coupling expansion of the thermodynamic Bethe-ansatz equations for the one-dimensional Hubbard model

Zou Ha

Published Nov 15, 1992• 6 citations
Publisher

Abstract

The ``string'' structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to suggest the validity of thermodynamic Bethe-ansatz equations (TBAE). We furthermore solve TBAE in a strong-coupling expansion series form and obtain the thermodynamic potential which agrees with the known high-temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some additional features of the strongly correlated one-dimensional Hubbard model.

DOI
10.1103/physrevb.46.12205

Related papers

Thermodynamic Bethe ansatz equations of one-dimensional Hubbard model and high-temperature expansion

Minoru Takahashi, Masahiro Shiroishi

A numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of the one-dimensional Hubbard model are numerically calculated and compared with high-temperature expansion and numerical results of the quantum transfer matrix method by J\"uttner, Kl\"umper, and Suzuki. The coincidence is surprisingly good. We obtain the high-temperature expansion of the grand potential up to ${\ensuremath{\beta}}^{6}.$

Physical review. B, Condensed matter•Apr 4, 2002•27 citations

TBA Equations of 1D Hubbard Model and High-Temperature Expansion

Minoru Takahashi, Masahiro Shiroishi

New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by Jüttner, Klümper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to $β^6$.

arXiv:cond-mat/0110645•Oct 31, 2001•2 citations

An Extension of the Thermal Bethe Ansatz: One-Dimensional Hubbard Model

Tohru Koma

The thermodynamics of the one-dimensional Hubbard model is reduced to a system of algebraic equations through an extension of our thermal Bethe ansatz. This new formalism is free from the string conjecture, or more basically from the unproven assumption of the completeness of the Bethe states.

Progress of Theoretical Physics•Apr 1, 1990•14 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

Thermodynamic Properties of One-Dimensional Hubbard Model at Finite Temperatures

Chi Yang, ARMEN N. KOCHARIAN, You-Ling Chiang

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.

International Journal of Modern Physics B•Aug 10, 2003•0 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
The ``string'' structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to suggest the validity of thermodynamic Bethe-ansatz equations (TBAE). We furthermore solve TBAE in a strong-coupling expansion series form and obtain the thermodynamic potential which agrees with the known high-temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some additional features of the strongly correlated one-dimensional Hubbard model.
New numerical method to calculate thermodynmic Bethe ansatz equations is proposed based on Newton's method. Thermodynamic quantities of one-dimensional Hubbard model is numerically calculated and compared with high temperature expansion and numerical results of quantum transfer matrix method by Jüttner, Klümper and Suzuki. The coincidence is surprisingly good. We get high-temperature expansion of grand potential up to β6β^6β6.
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.
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.
[[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.