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

• Published in: Journal of Statistical Mechanics: Theory and Experiment
• Main Author: Stéphan, Jean-Marie
• Other Authors: Probabilités, statistique, physique mathématique (PSPM), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2017
• Subjects: [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]; [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el]; Arctic
• Online Access: https://hal.science/hal-01654901; https://doi.org/10.1088/1742-5468/aa8c19

International audience We study the return probability and its imaginary ($\tau$) time continuation after a quench from a domain wall initial state in the XXZ spin chain, focusing mainly on the region with anisotropy $|\Delta|< 1$. 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 $\tau^2$, which reflects the fact that the model exhibits the limit shape phenomenon. In real time, we observe that in the region $|\Delta|<1$ 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 $x_{\rm f}(t)=t\sqrt{1-\Delta^2}$, by analytic continuation of known arctic curves in the six vertex model. Exactly at $|\Delta|=1$, we find the return probability decays as $e^{-\zeta(3/2) \sqrt{t/\pi}}t^{1/2}O(1)$. 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.