Quantum Quenches in an XXZ Spin Chain with an Inhomogeneous Initial State

We present results for the non-equilibrium dynamics of a quantum \textit{XXZ} spin chain, whose spins are initially arranged in a domain wall profile, via the application of a spatially-varying magnetic field in the $z$-direction. The system is driven out of equilibrium by rapidly turning off the magnetic field, leaving the system in a highly excited state. We study the time-evolution of the domain wall profile and various two-point correlation functions. The results are obtained both numerically and analytically via a bosonization approach. For the case of the \textit{XX} chain, which maps onto a model of non-interacting fermions, we find an interesting even-odd dichotomy in the long-time behavior of the transverse correlation function for sites spaced by $n$ lattice points. For the \textit{XXZ} chain, we highlight how the domain wall dynamics depend on whether the system is in the gapless \textit{XX} phase or in the gapped, Ising phase.