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/9608026

The 1/r2 t-J model in a magnetic field

J. T. Liu, D. F. Wang

Published Aug 6, 1996• 0 citations
arXivHTMLPDF

Abstract

We study the one-dimensional supersymmetric t-J model with 1/r2 interaction threaded by magnetic flux. Because of the long range interaction, the effect of this flux leads to a modification of the electron hopping term. We present an exact solution of this model for all values of the flux, concisely formulated as a set of Bethe-ansatz-like equations. This allows a computation of the persistent currents at zero temperature. It is found that the system violates Leggett's conjecture despite the fact that the long range t-J model is a special example of the Luttinger liquid university class.

DOI
10.48550/arxiv.cond-mat/9608026

Related papers

1/r2t - J model in a magnetic field

James T. Liu, D. F. Wang

We study the one-dimensional supersymmetric $t$-$J$ model with ${1/r}^{2}$ interaction threaded by magnetic flux. Because of the long-range interaction, the effect of this flux leads to a modification of the electron hopping term. We present an exact solution of this model for all values of the flux, concisely formulated as a set of Bethe-ansatz-like equations. Examination of the ground state shows that the persistent currents at zero temperature do not exhibit a parity effect despite the fact that the long-range $t$-$J$ model falls in the Luttinger-liquid universality class. This exception to Leggett's conjecture arises because of the special nature of the long-range hopping.

Physical review. B, Condensed matter•Aug 1, 1997•3 citations

Spectrum and thermodynamics of the one-dimensional supersymmetrict-Jmodel with 1/ r2 exchange and hopping

D. F. Wang, James T. Liu, Piers Coleman

We derive the spectrum and thermodynamics of the one-dimensional supersymmetric t-J model with long-range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirically determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.

arXiv:cond-mat/9312019•Physical review. B, Condensed matter•Sep 1, 1992•50 citations

Spectrum and thermodynamics of the one-dimensional supersymmetric t - J model with 1/ r 2 exchange and hopping

James T. Liu, P. Coleman, D. F. Wang

We derive the spectrum and the thermodynamics of the one-dimensional supersymmetric t-J model with long range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.

•Jul 2, 2021•0 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

Thermodynamics of an integrable model for electrons with correlated hopping

Gerald Bedürftig, Holger Frahm

A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.

arXiv:cond-mat/9504103•Journal of Physics A Mathematical and General•Aug 21, 1995•41 citations

Low-temperature specific heat of the degenerate supersymmetric t-J model in one dimension

Kong-Ju-Bock Lee, P. Schlottmann

We consider the one-dimensional SU(N)-invariant t-J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin-exchange J between neighboring lattice sites. The model is integrable and has been diagonalized in terms of nested Bethe ansatze at the supersymmetric point t=J. The low-T specific heat is proportional to T. The γ-coefficient is extracted from the thermodynamic Bethe-ansatz equations and is expressed in terms of the spin wave velocities and the group velocity of the charges for arbitrary N, band filling, and splitting of the levels (magnetic and crystalline fields). Our results contain the following special cases: (i) For N=2 the traditional spin-1/2 supersymmetric t-J model, (ii) for exactly one electron per site the SU(N)-Heisenberg chain, and (iii) for N=4 the two-band supersymmetric t-J model with crystalline field splitting.

Journal of Applied Physics•Apr 15, 1996•1 citation
We study the one-dimensional supersymmetric t-J model with 1/r2 interaction threaded by magnetic flux. Because of the long range interaction, the effect of this flux leads to a modification of the electron hopping term. We present an exact solution of this model for all values of the flux, concisely formulated as a set of Bethe-ansatz-like equations. This allows a computation of the persistent currents at zero temperature. It is found that the system violates Leggett's conjecture despite the fact that the long range t-J model is a special example of the Luttinger liquid university class.
We study the one-dimensional supersymmetric ttt-JJJ model with 1/r2{1/r}^{2}1/r2 interaction threaded by magnetic flux. Because of the long-range interaction, the effect of this flux leads to a modification of the electron hopping term. We present an exact solution of this model for all values of the flux, concisely formulated as a set of Bethe-ansatz-like equations. Examination of the ground state shows that the persistent currents at zero temperature do not exhibit a parity effect despite the fact that the long-range ttt-JJJ model falls in the Luttinger-liquid universality class. This exception to Leggett's conjecture arises because of the special nature of the long-range hopping.
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.
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe ansatz. We investigate the phase diagram of this model by studying the ground state and excitations of the model as a function of the interaction parameter, electronic density and magnetization. Using arguments from conformal field theory we can study the critical exponents describing the asymptotic behaviour of correlation functions at long distances.
We consider the one-dimensional SU(N)-invariant t-J model, which consists of electrons with N spin components on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites and spin-exchange J between neighboring lattice sites. The model is integrable and has been diagonalized in terms of nested Bethe ansatze at the supersymmetric point t=J. The low-T specific heat is proportional to T. The γ-coefficient is extracted from the thermodynamic Bethe-ansatz equations and is expressed in terms of the spin wave velocities and the group velocity of the charges for arbitrary N, band filling, and splitting of the levels (magnetic and crystalline fields). Our results contain the following special cases: (i) For N=2 the traditional spin-1/2 supersymmetric t-J model, (ii) for exactly one electron per site the SU(N)-Heisenberg chain, and (iii) for N=4 the two-band supersymmetric t-J model with crystalline field splitting.