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Determinant Representation of Correlation Functions for the $U_q(gl(1|1))$ Free Fermion Model

Shao-you Zhao A, Wen‐Li Yang, Yao-Zhong Zhang

Published Jun 9, 2005• 7 citations
OpenAlex

Abstract

With the help of the factorizing $F$-matrix, the scalar products of the $U_q(gl(1|1))$ free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.

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Determinant Representation of Correlation Functions for the Uq(gl(1∣1))U_q(gl(1|1))Uq​(gl(1∣1)) Free Fermion Model
With the help of the factorizing FFF-matrix, the scalar products of the Uq(gl(1∣1))U_q(gl(1|1))Uq​(gl(1∣1)) free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model.
Working in the F-basis provided by the factorizing F-matrix, the scalar products of Bethe states for the supersymmetric t-J model are represented by determinants. By means of these results, we obtain determinant representations of correlation functions The computation of correlation functions is one of the major challenging problems in the theory of quantum integrable models [1, 2]. There are currently two approaches for computing the correlation functions of a quantum integrable model. One is the vertex operator method (see e.g. [3-8]), and another one is based on the detailed analysis of the structure of
We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the Uq(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.
We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing FFF-matrices (or the so-called FFF-basis) play an important role in the construction. In the FFF-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the gl\\glgl (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analysing physical properties of the integrable models in the thermodynamical limit.