Exact time evolution formulae in the XXZ spin chain with domain wall initial state

Abstract

We study the time evolution of the spin-1/2 XXZ chain initialized in a domain wall state, where all spins to the left of the origin are up, all spins to its right are down. The focus is on exact formulae, which hold for arbitrary finite (real or imaginary) time. In particular, we compute the amplitudes corresponding to the process where all but $k$ spins come back to their initial orientation, as a $k-$fold contour integral. These results are obtained using a correspondence with the six vertex model, and taking a somewhat complicated Hamiltonian/Trotter-type limit. Several simple applications are studied and also discussed in a broader context.

Hydrodynamics of low-dimensional quantum systems

“…I fact, it is often useful to go back to the classical realm, in order to disentangle classical form quantum effects. In this special issue, contributions developed the hydrodynamic theory of integrable systems either quite generally [9,13], or by focussing on gases of particles [6,24], quantum spin systems [27], quantum and classical field theories [2,16,19], and even cellular automata [15,17,18,21,23] and ensembles of classical solitons of integrable partial differential equations [5,28]. Third, of particular interest in one-dimensional quantum systems is their often very peculiar or anomalous transport properties.…”