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

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.