On the Construction of Correlation Functions for the Integrable Supersymmetric Fermion Models

TL;DR

This paper reviews the recent development of determinant formulas for correlation functions in integrable supersymmetric fermion models, emphasizing the role of $F$-matrices and symmetric Bethe states.

Contribution

It introduces a method to construct determinant representations of correlation functions using $F$-matrices and symmetric Bethe states for supersymmetric fermion models.

Findings

Determinant representations of two-point correlation functions are derived.

The approach simplifies analysis of physical properties in the thermodynamic limit.

The method applies to the $ ext{gl}(2|1)$ supersymmetric t-J model.

Abstract

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 $\gl$ (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.