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Article Dans Une Revue Journal of Statistical Mechanics: Theory and Experiment Année : 2017

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

Résumé

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.

Dates et versions

hal-01654901 , version 1 (04-12-2017)

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Jean-Marie Stéphan. Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain. Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017 (10), ⟨10.1088/1742-5468/aa8c19⟩. ⟨hal-01654901⟩
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