Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons

TL;DR

This paper derives an exact analytical formula for the time evolution of the one-body density matrix in a one-dimensional hard-core boson system after an interaction quench, enabling precise numerical analysis in the thermodynamic limit.

Contribution

It provides the first exact analytical expression for the post-quench dynamics of the one-body density matrix in the Lieb-Liniger model at infinite repulsion.

Findings

Expression involves difference of two Fredholm determinants

Valid for all times after the quench in the thermodynamic limit

Numerically evaluable for practical computations

Abstract

We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there exists a mapping between the bosonic wavefuntions and the free fermionic ones but this does not help the computation of the one-body density matrix which is sensitive to particle statistics. The final expression, given in terms of the difference of the square root of two Fredholm determinants, can be numerically evaluated and is valid in the thermodynamic limit and for all times after the quench.