Journal of the Physical Society of Japan

SU(N) Calogero-Sutherland Model andt-JModelwith 1/x2Interaction

Norio Kawakami

Published Jul 15, 1993• 15 citations

Abstract

The asymptotic Bethe-ansatz (ABA) solution is obtained for the one-dimensional SU( N ) Calogero-Sutherland model and the SU( N ) t - J model with 1/ x 2 long-range interaction. Bulk quantities and correlation exponents are computed. The results reproduce those obtained by Ha and Haldane using the exact Jastrow-type eigenfunctions. The ABA solution enables a simple and systematic treatment of the energy spectrum of the above models.

DOI: 10.1143/jpsj.62.2270

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Journal of the Physical Society of Japan

SU(N) Calogero-Sutherland Model andt-JModelwith 1/x2Interaction

Norio Kawakami

Published Jul 15, 1993• 15 citations

Publisher

Abstract

DOI: 10.1143/jpsj.62.2270

Related papers

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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.

An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/

{\mathit{r}}^{2}

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/

{\mathit{r}}^{2}

The S=1/2 Heisenberg Hamiltonian H=1/2${\mathcal{J}}_{\mathrm{n}=1}^{\mathrm{N}\mathrm{\ensuremath{-}}1}$

{\mathcal{J}}_{\mathit{m}=1}^{\mathit{N}}

{\mathit{J}}_{\mathit{n}}

${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}}$\ensuremath{\cdot} ${\mathrm{\ensuremath{\sigma}}}_{\mathit{m}+\mathit{n}}$, with

{J}_{n}

{J}_{0}

{\mathrm{sin}}^{2}

(n\ensuremath{\pi}/N), is shown to have a simple singlet ground state in the form of a Jastrow function. The spectrum and correlations are explicitly known and the magnetic susceptibility is shown to be Pauli type at T=0. The model has a striking similarity to the nearest-neighbor isotropic Heisenberg model and may be viewed as a discretized version of the Sutherland-Calogero-Moser system.