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Physical review. B, Condensed matter

Asymptotic Bethe-ansatz solution of multicomponent quantum systems with 1r2 long-range interaction

Norio Kawakami

Published Jul 1, 1992• 119 citations
Publisher

Abstract

Asymptotic Bethe-ansatz solutions are obtained for one-dimensional quantum systems with a $\frac{1}{{r}^{2}}$ long-range interaction by generalizing Sutherland's method to multicomponent quantum systems. We obtain the solutions to the supersymmetric $t\ensuremath{-}J$ model of Kuramoto and Yokoyama, the $\mathrm{SU}(\ensuremath{\nu})$ Haldane-Shastry model, and the multicomponent $t\ensuremath{-}J$ model. The excitation spectrum as well as bulk quantities are computed analytically. Conformal properties of low-energy excitations are discussed in connection with Luttinger liquid theory.

DOI
10.1103/physrevb.46.1005

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Asymptotic Bethe-ansatz solutions are obtained for one-dimensional quantum systems with a 1r2\frac{1}{{r}^{2}}r21​ long-range interaction by generalizing Sutherland's method to multicomponent quantum systems. We obtain the solutions to the supersymmetric t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model of Kuramoto and Yokoyama, the SU(\ensuremathν)\mathrm{SU}(\ensuremath{\nu})SU(\ensuremathν) Haldane-Shastry model, and the multicomponent t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model. The excitation spectrum as well as bulk quantities are computed analytically. Conformal properties of low-energy excitations are discussed in connection with Luttinger liquid theory.
An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/r2{\mathit{r}}^{2}r2 long-range exchange and transfer, for which the ground-state wave function was obtained exactly by Kuramoto and Yokoyama. The present approach makes it possible to study analytically the energy spectrum as well as bulk quantities. The calculated quantities reproduce the exact results known for low-temperature properties and correlation functions. This solution represents an application for the asymptotic Bethe ansatz to correlated electron systems.
An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/r2{\mathit{r}}^{2}r2 long-range exchange and transfer, for which the ground-state wave function was obtained exactly by Kuramoto and Yokoyama. The present approach makes it possible to study analytically the energy spectrum as well as bulk quantities. The calculated quantities reproduce the exact results known for low-temperature properties and correlation functions. This solution represents an application for the asymptotic Bethe ansatz to correlated electron systems.
Finite-size scaling analysis is performed for one-dimensional Bose and Fermi systems with long-range interaction g/r2{\mathit{r}}^{2}r2, based on the exact solution of Sutherland. The low-energy behavior of this model is shown to be described by the c=1 conformal field theory. Exact formulas for various correlation exponents are obtained. At a special point g=4, the model belongs to the same universality class as the Haldane-Shastry model, the effective theory of which is the level-1 SU(2) Kac-Moody theory.
We review recent results obtained for a class of one-dimensional quantum models with 1/r2 long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU(ν) spin chain, the OSp(ν, 1) supersymmetric t-J model and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of 1/r2 models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.
We review recent results obtained for a class of one-dimensional quantum models with 1/r2 long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU(ν) spin chain, the OSp(ν, 1) supersymmetric t-J model and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of 1/r2 models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.