Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain. (30th October 2017) - Stéphan, Jean-Marie
Abstract: We study the return probability and its imaginary ( τ ) time continuation after a quench from a domain wall initial state in the XXZ spin chain, focusing mainly on the region with anisotropy | Δ | < 1 . We establish exact Fredholm determinant formulas for those, by exploiting a connection to the six-vertex model with domain wall boundary conditions. In imaginary time, we find the expected scaling for a partition function of a statistical mechanical model of area proportional to τ 2, which reflects the fact that the model exhibits the limit shape phenomenon. In real time, we observe that in the region | Δ | < 1 the decay for long time t is nowhere continuous as a function of anisotropy: it is Gaussian at roots of unity and exponential otherwise. We also determine that the front moves as x f ( t ) = t 1 − Δ 2, by the analytic continuation of known arctic curves in the six-vertex model. Exactly at | Δ | = 1, we find the return probability decays as e − ζ ( 3 / 2 ) t / π t 1 / 2 O ( 1 ) . It is argued that this result provides an upper bound on spin transport. In particular, it suggests that transport should be diffusive at the isotropic point for this quench.