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

Zvonarev, M. B. and Cheianov, Vadim and Giamarchi, T. (2009) The time-dependent correlation function of the Jordan-Wigner operator as a Fredholm determinant. Journal of Statistical Mechanics: Theory and Experiment. -. ISSN 1742-5468

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 the literature for treating similar problems.