Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain

• Main Author: Stéphan, Jean-Marie
• Format: Text
• Language: unknown
• Published: arXiv 2017
• Subjects: Statistical Mechanics cond-mat.stat-mech; Strongly Correlated Electrons cond-mat.str-el; FOS Physical sciences; Arctic
• Online Access: https://dx.doi.org/10.48550/arxiv.1707.06625; https://arxiv.org/abs/1707.06625

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 large times $t$ is nowhere continuous as a function of anisotropy: it is either gaussian at root of unity or exponential otherwise. As an aside, we also determine that the front moves as $x_{\rm f}(t)=t\sqrt{1-Δ^2}$, by analytic continuation of known arctic curves in the six vertex model. Exactly at $|Δ|=1$, we find the return probability decays as $e^{-ζ(3/2) \sqrt{t/π}}t^{1/2}O(1)$. 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. : 33 pages, 8 figures. v2: typos fixed, references added. v3: minor changes