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

Journal of Statistical Mechanics Theory and Experiment

Bosonization and correlators of the one-dimensional Hubbard model

Alexander A. Ovchinnikov

Published Oct 29, 2024• 0 citations
Publisher

Abstract

Abstract We present a simple derivation of the Luttinger liquid relation for the one-dimensional Hubbard model, considering a finite U and in the U = ∞ limit. We describe a simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and physical way using the bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary U through a single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and physically transparent way.

DOI
10.1088/1742-5468/ad83c6

Related papers

Bosonization and correlators of the one-dimensional Hubbard model

А. А. Овчинников

We present simple derivation of the Luttinger liquid relation for the 1D Hubbard model both for finite $U$ and in the $U=\infty$ limit. We describe the simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and a physical way using the Bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary $U$ through the single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and a physically transparent way.

arXiv:2410.22610•Oct 30, 2024•0 citations

Bosonization Based on Bethe Ansatz Equations and Spin-Charge Separation in the Hubbard Model with Finite U

Yue Yu, Huan-Xiong Yang, Yong-Shi Wu

We develop a bosonization approach for one-dimensional models based on Bethe ansatz equations. The operator formalism of the exact soluble models in the low energy limit provides a systematic method to calculate the asymptotic correlation functions. As examples with and without internal degrees of freedom, the Calogero-Sutherland (C-S) model and the repulsive Hubbard model are considered respectively. We verify that the low energy behavior of the C-S model is controlled by two classes of c=1 conformal field theories, depending on whether the C-S interactions are among bosons or among fermions. For the Hubbard model, we show the explicit charge-spin separation at low energy for arbitrary U>0. The low energy behavior of the system is described by the (semi-) direct product of two independent Virasoro algebras with c=1.

arXiv:cond-mat/9911141•Nov 10, 1999•1 citation

Luttinger liquid properties of highly correlated electron systems in one dimension

Norio Kawakami, Sung-Kil Yang

An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.

Advanced series in mathematical physics•May 1, 1994•0 citations

Luttinger liquid properties of highly correlated electron systems in one dimension

N. Kawakami, Sung-Kil Yang

An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.

Journal of Physics Condensed Matter•Aug 12, 1991•74 citations

Exact Results for Highly Correlated Electron Systems in One Dimension

P. Schlottmann

One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.

International Journal of Modern Physics B•Feb 20, 1997•143 citations

Critical exponents for the one-dimensional Hubbard model

Holger Frahm, V. E. Korepin

Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.

Physical review. B, Condensed matter•Dec 1, 1990•502 citations
Abstract We present a simple derivation of the Luttinger liquid relation for the one-dimensional Hubbard model, considering a finite U and in the U = ∞ limit. We describe a simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and physical way using the bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary U through a single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and physically transparent way.
We present simple derivation of the Luttinger liquid relation for the 1D Hubbard model both for finite UUU and in the U=∞U=\inftyU=∞ limit. We describe the simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and a physical way using the Bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary UUU through the single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and a physically transparent way.
We develop a bosonization approach for one-dimensional models based on Bethe ansatz equations. The operator formalism of the exact soluble models in the low energy limit provides a systematic method to calculate the asymptotic correlation functions. As examples with and without internal degrees of freedom, the Calogero-Sutherland (C-S) model and the repulsive Hubbard model are considered respectively. We verify that the low energy behavior of the C-S model is controlled by two classes of c=1 conformal field theories, depending on whether the C-S interactions are among bosons or among fermions. For the Hubbard model, we show the explicit charge-spin separation at low energy for arbitrary U>0. The low energy behavior of the system is described by the (semi-) direct product of two independent Virasoro algebras with c=1.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
An exact description is given of the long-distance behaviour of the one-dimensional t-J model at t=J. The authors employ the Bathe ansatz method and the finite-size scaling technique in conformal field theory. The charge and spin degrees of freedom are separated, and described by two independent c=1 conformal theories. The critical exponents for the charge, spin, electron and superconducting correlation functions are obtained for arbitrary band filling. The authors then make detailed comparison of the t-J model with the repulsive Hubbard model with emphasis on the Luttinger liquid properties. Analysing the electron filling dependence they observe the enhancement of the superconducting correlations compared with the highly correlated Hubbard model. The effect of the external magnetic field at and near half-filling is also discussed.
One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.
Using results on the scaling of energies with the size of the system and the principles of conformal quantum field theory, we calculate the asymptotics of correlation functions for the one-dimensional Hubbard model in the repulsive regime in the presence of an external magnetic field. The critical exponents are given in terms of a dressed charge matrix that is defined in terms of a set of integral equations obtained from the Bethe-Ansatz solution for the Hubbard model. An interpretation of this matrix in terms of thermodynamical coefficients is given, and several limiting cases are considered.