Time-dependent correlation function of the Jordan-Wigner operator as a Fredholm determinant

TL;DR

This paper derives a Fredholm determinant representation for the time-dependent correlation function of the Jordan-Wigner operator in free-fermion models, facilitating analytic and numerical analysis.

Contribution

It introduces a novel Fredholm determinant formulation that bypasses form-factor summations for calculating correlations in free-fermion systems.

Findings

Determinant representation simplifies correlation calculations.

Enables efficient analytic and numerical evaluations.

Provides a new approach for studying quantum correlations.

Abstract

We calculate a correlation function of the Jordan-Wigner operator in a class of free-fermion models formulated on an infinite one-dimensional lattice. We represent this function in terms of the determinant of an integrable Fredholm operator, convenient for analytic and numerical investigations. By using Wick's theorem, we avoid the form-factor summation customarily used in literature for treating similar problems.