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

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.

Latex file, 42 pages. Invited review article for Int. J. Mod. Phys. B; V2: Two references added, mionor typos corrected

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Cited by in corpus (7)

• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms
• Scalar products of the open XYZ chain with non-diagonal boundary terms
• Drinfeld twists of the open XXZ chain with non-diagonal boundary terms
• Determinant formula for the partition function of the six-vertex model with a non-diagonal reflecting end
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• A convenient basis for the Izergin-Korepin model
• Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms