Inhomogeneous field theory inside the arctic circle
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a cr...
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ftdatacite:10.48550/arxiv.1512.02872 2023-05-15T14:59:16+02:00 Inhomogeneous field theory inside the arctic circle Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo 2015 https://dx.doi.org/10.48550/arxiv.1512.02872 https://arxiv.org/abs/1512.02872 unknown arXiv https://dx.doi.org/10.1088/1742-5468/2016/05/053108 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 Mathematical Physics math-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2015 ftdatacite https://doi.org/10.48550/arxiv.1512.02872 https://doi.org/10.1088/1742-5468/2016/05/053108 2022-04-01T11:41:24Z Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac field theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point ($Δ=0$). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix. : 62 pages, 17 figures, 3 tables. Published version 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 Mathematical Physics math-ph FOS Physical sciences |
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Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el Mathematical Physics math-ph FOS Physical sciences Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo Inhomogeneous field theory inside the arctic circle |
topic_facet |
Statistical Mechanics cond-mat.stat-mech Strongly Correlated Electrons cond-mat.str-el Mathematical Physics math-ph FOS Physical sciences |
description |
Motivated by quantum quenches in spin chains, a one-dimensional toy-model of fermionic particles evolving in imaginary-time from a domain-wall initial state is solved. The main interest of this toy-model is that it exhibits the arctic circle phenomenon, namely a spatial phase separation between a critically fluctuating region and a frozen region. Large-scale correlations inside the critical region are expressed in terms of correlators in a (euclidean) two-dimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac field theory in curved space. The technique used to solve the toy-model is then extended to deal with the transfer matrices of other models: dimers on the honeycomb and square lattice, and the six-vertex model at the free fermion point ($Δ=0$). In all cases, explicit expressions are given for the long-range correlations in the critical region, as well as for the underlying Dirac action. Although the setup developed here is heavily based on fermionic observables, the results can be translated into the language of height configurations and of the gaussian free field, via bosonization. Correlations close to the phase boundary and the generic appearance of Airy processes in all these models are also briefly revisited in the appendix. : 62 pages, 17 figures, 3 tables. Published version |
format |
Text |
author |
Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo |
author_facet |
Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo |
author_sort |
Allegra, Nicolas |
title |
Inhomogeneous field theory inside the arctic circle |
title_short |
Inhomogeneous field theory inside the arctic circle |
title_full |
Inhomogeneous field theory inside the arctic circle |
title_fullStr |
Inhomogeneous field theory inside the arctic circle |
title_full_unstemmed |
Inhomogeneous field theory inside the arctic circle |
title_sort |
inhomogeneous field theory inside the arctic circle |
publisher |
arXiv |
publishDate |
2015 |
url |
https://dx.doi.org/10.48550/arxiv.1512.02872 https://arxiv.org/abs/1512.02872 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
https://dx.doi.org/10.1088/1742-5468/2016/05/053108 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1512.02872 https://doi.org/10.1088/1742-5468/2016/05/053108 |
_version_ |
1766331380061437952 |