Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
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 ex...
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ftunivlyon:oai:HAL:hal-01654901v1 2024-09-09T19:26:36+00:00 Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain Stéphan, Jean-Marie 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) 2017-10-30 https://hal.science/hal-01654901 https://doi.org/10.1088/1742-5468/aa8c19 en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/arxiv/1707.06625 info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/aa8c19 hal-01654901 https://hal.science/hal-01654901 ARXIV: 1707.06625 doi:10.1088/1742-5468/aa8c19 ISSN: 1742-5468 Journal of Statistical Mechanics: Theory and Experiment https://hal.science/hal-01654901 Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017 (10), ⟨10.1088/1742-5468/aa8c19⟩ [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] info:eu-repo/semantics/article Journal articles 2017 ftunivlyon https://doi.org/10.1088/1742-5468/aa8c19 2024-07-08T23:59:56Z 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. Article in Journal/Newspaper Arctic Université de Lyon: HAL Arctic Journal of Statistical Mechanics: Theory and Experiment 2017 10 103108 |
institution |
Open Polar |
collection |
Université de Lyon: HAL |
op_collection_id |
ftunivlyon |
language |
English |
topic |
[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] |
spellingShingle |
[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] Stéphan, Jean-Marie Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain |
topic_facet |
[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] |
description |
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. |
author2 |
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 |
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 |
HAL CCSD |
publishDate |
2017 |
url |
https://hal.science/hal-01654901 https://doi.org/10.1088/1742-5468/aa8c19 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 1742-5468 Journal of Statistical Mechanics: Theory and Experiment https://hal.science/hal-01654901 Journal of Statistical Mechanics: Theory and Experiment, 2017, 2017 (10), ⟨10.1088/1742-5468/aa8c19⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/1707.06625 info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/aa8c19 hal-01654901 https://hal.science/hal-01654901 ARXIV: 1707.06625 doi:10.1088/1742-5468/aa8c19 |
op_doi |
https://doi.org/10.1088/1742-5468/aa8c19 |
container_title |
Journal of Statistical Mechanics: Theory and Experiment |
container_volume |
2017 |
container_issue |
10 |
container_start_page |
103108 |
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1809896183195238400 |