Return amplitude after a quantum quench in the XY chain

We determine an exact formula for the transition amplitude between any two arbitrary eigenstates of the local z-magnetization operators in the quantum XY chain. We further use this formula to obtain an analytical expression for the return amplitude of fully polarized states and the Neel state on a ring of length L. Then, we investigate finite-size effects in the return amplitude: in particular quasi-particle interference halfway along the ring, a phenomenon that has been dubbed traversal (Essler and Fagotti 2016 J. Stat. Mech. 064002). We show that the traversal time and the features of the return amplitude at the traversal time depend on the initial state and on the parity of L. Finally, we briefly discuss non-analyticities in time of the decay rates in the thermodynamic limit L -> infinity, which are known as dynamical phase transitions.