Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
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 si...
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ftdatacite:10.48550/arxiv.1707.06625 2023-05-15T15:09:41+02:00 Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain Stéphan, Jean-Marie 2017 https://dx.doi.org/10.48550/arxiv.1707.06625 https://arxiv.org/abs/1707.06625 unknown arXiv https://dx.doi.org/10.1088/1742-5468/aa8c19 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el FOS Physical sciences article-journal Article ScholarlyArticle Text 2017 ftdatacite https://doi.org/10.48550/arxiv.1707.06625 https://doi.org/10.1088/1742-5468/aa8c19 2022-04-01T10:28:58Z 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 Text Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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topic |
Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el FOS Physical sciences |
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Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el FOS Physical sciences Stéphan, Jean-Marie Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
topic_facet |
Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el FOS Physical sciences |
description |
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 |
format |
Text |
author |
Stéphan, Jean-Marie |
author_facet |
Stéphan, Jean-Marie |
author_sort |
Stéphan, Jean-Marie |
title |
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
title_short |
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
title_full |
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
title_fullStr |
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
title_full_unstemmed |
Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
title_sort |
return probability after a quench from a domain wall initial state in the spin-1/2 xxz chain |
publisher |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1707.06625 https://arxiv.org/abs/1707.06625 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
https://dx.doi.org/10.1088/1742-5468/aa8c19 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1707.06625 https://doi.org/10.1088/1742-5468/aa8c19 |
_version_ |
1766340824934645760 |