Asymptotic Bethe-ansatz solution of multicomponent quantum systems with <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mrow><mn>1</mn></mrow><mrow><mrow><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></mfrac></math></span> long-range interaction

Norio Kawakami

doi:10.1103/PhysRevB.46.1005

Asymptotic Bethe-ansatz solution of multicomponent quantum systems with $\frac{1}{r^{2}}$ long-range interaction

Norio Kawakami^*

Max-Planck-Institut für Festkörperforschung, 7000 Stuttgart 80, Germany
Theoretische Physik, Eidgenössische Technische Hochschule, Höngerberg 8093 Zürich, Switzerland

^*On leave from Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606, Japan.

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Phys. Rev. B 46, 1005 – Published 1 July, 1992

DOI: https://doi.org/10.1103/PhysRevB.46.1005

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 $t - J$ model of Kuramoto and Yokoyama, the $SU (ν)$ Haldane-Shastry model, and the multicomponent $t - J$ 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.

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Physical Review B

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Asymptotic Bethe-ansatz solution of multicomponent quantum systems with $\frac{1}{r^{2}}$ long-range interaction

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

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Asymptotic Bethe-ansatz solution of multicomponent quantum systems with $\frac{1}{r^{2}}$ long-range interaction