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Acta Physica Sinica

HIDDEN LOCAL GAUGE INVARIANCE IN FATEEV-ZAMOLO-DCHIKOV QUANTUM SPIN CHAIN

GUAN XI-WEN, Zhuang Xiong, Huan-Qiang Zhou, 四川师范大学物理系,成都610066

Published Jan 1, 1993• 1 citation
Publisher

Abstract

Hidden local gauge invariance in Fateev-Zamolodchikov quantum spin chain is studied in detail in the framework of the quantum inverse scattering method (QISM). It is found that, similar to the case of spin 1/2, this model admits an Abelian U(1) gauge transformation and that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent.

DOI
10.7498/aps.42.331

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Hidden local gauge invariance in Fateev-Zamolodchikov quantum spin chain is studied in detail in the framework of the quantum inverse scattering method (QISM). It is found that, similar to the case of spin 1/2, this model admits an Abelian U(1) gauge transformation and that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent.
Hidden local gauge invariance in the one-dimensional (1-D) Hubbard model and its equivalent coupled spin model is studied. It is found that Abelian U(1)⊗U(1) gauge transformations appear in both cases. Furthermore, it is shown that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent. However, this result relies heavily on Shastry’s conjecture about the eigenvalue of the transfer matrix for the 1-D Hubbard model. Lastly, there is also a discrete symmetry associated to Z2⊗Z2. Once this symmetry is broken, one immediately obtains another nontrivial solution to the Yang–Baxter relations. UFaipxr
The sector of zero ZN charge is studied for the ferromagnetic (FM) and antiferromagnetic (AFM) version of the (ZN×Z2)-invariant Fateev-Zamolodchikov quantum spin chain. We conjecture that the relevant Bethe ansatz equations should admit, besides the usual stringlike solutions, exceptional multiplets, and a number of nonphysical solutions. Once the physical ones are identified, we show how completeness and the gapless excitation spectrum can be obtained. The central charge is computed from the specific heat and found to be [Formula: see text] (FM) and c=1 (AFM).