Normal Ordering in the Theory of Correlation Functions of Exactly Solvable Models

TL;DR

This paper develops a method using auxiliary Fock space and determinant representations to compute asymptotic correlation functions in exactly solvable quantum models solved by the algebraic Bethe ansatz.

Contribution

It introduces a novel approach to calculate the asymptotic behavior of correlation functions via Fredholm determinants and auxiliary Bose fields.

Findings

Determinant representations simplify correlation function calculations.

Auxiliary Fock space facilitates asymptotic analysis.

Method applies to models solvable by algebraic Bethe ansatz.

Abstract

We study models of quantum statistical mechanics which can be solved by the algebraic Bethe ansatz. The general method of calculation of correlation functions is based on the method of determinant representations. The auxiliary Fock space and auxiliary Bose fields are introduced in order to remove the two body scattering and represent correlation functions as a mean value of a determinant of a Fredholm integral operator; the representation has a simple form for large space and time separations. In this paper we explain how to calculate the mean value in the auxiliary Fock space of asymptotic expression of the Fredholm determinant. It is necessary for the evaluation of the asymptotic form of the physical correlation functions.