Inhomogeneous field theory inside the arctic circle
International audience 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...
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Online Access: | https://hal.archives-ouvertes.fr/hal-01586415 https://doi.org/10.1088/1742-5468/2016/05/053108 |
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ftccsdartic:oai:HAL:hal-01586415v1 2023-05-15T14:59:24+02:00 Inhomogeneous field theory inside the arctic circle Allegra, Nicolas Dubail, Jerome Stéphan, Jean-Marie Viti, Jacopo Institut Jean Lamour (IJL) Institut de Chimie du CNRS (INC)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) Max Planck Institute for the Physics of Complex Systems (MPI-PKS) Max-Planck-Gesellschaft 2016 https://hal.archives-ouvertes.fr/hal-01586415 https://doi.org/10.1088/1742-5468/2016/05/053108 en eng HAL CCSD IOP Publishing info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2016/05/053108 info:eu-repo/semantics/altIdentifier/arxiv/1512.02872 hal-01586415 https://hal.archives-ouvertes.fr/hal-01586415 doi:10.1088/1742-5468/2016/05/053108 ARXIV: 1512.02872 ISSN: 1742-5468 Journal of Statistical Mechanics: Theory and Experiment https://hal.archives-ouvertes.fr/hal-01586415 Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2016, 2016 (5), pp.053108. ⟨10.1088/1742-5468/2016/05/053108⟩ [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] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] info:eu-repo/semantics/article Journal articles 2016 ftccsdartic https://doi.org/10.1088/1742-5468/2016/05/053108 2021-12-19T02:32:22Z International audience 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 ($\Delta=0$). 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. Article in Journal/Newspaper Arctic Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Arctic Journal of Statistical Mechanics: Theory and Experiment 2016 5 053108 |
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Open Polar |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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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] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] |
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] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] Allegra, Nicolas Dubail, Jerome Stéphan, Jean-Marie Viti, Jacopo Inhomogeneous field theory inside the arctic circle |
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] [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] |
description |
International audience 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 ($\Delta=0$). 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. |
author2 |
Institut Jean Lamour (IJL) Institut de Chimie du CNRS (INC)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS) Max Planck Institute for the Physics of Complex Systems (MPI-PKS) Max-Planck-Gesellschaft |
format |
Article in Journal/Newspaper |
author |
Allegra, Nicolas Dubail, Jerome Stéphan, Jean-Marie Viti, Jacopo |
author_facet |
Allegra, Nicolas Dubail, Jerome 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 |
HAL CCSD |
publishDate |
2016 |
url |
https://hal.archives-ouvertes.fr/hal-01586415 https://doi.org/10.1088/1742-5468/2016/05/053108 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
ISSN: 1742-5468 Journal of Statistical Mechanics: Theory and Experiment https://hal.archives-ouvertes.fr/hal-01586415 Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2016, 2016 (5), pp.053108. ⟨10.1088/1742-5468/2016/05/053108⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/2016/05/053108 info:eu-repo/semantics/altIdentifier/arxiv/1512.02872 hal-01586415 https://hal.archives-ouvertes.fr/hal-01586415 doi:10.1088/1742-5468/2016/05/053108 ARXIV: 1512.02872 |
op_doi |
https://doi.org/10.1088/1742-5468/2016/05/053108 |
container_title |
Journal of Statistical Mechanics: Theory and Experiment |
container_volume |
2016 |
container_issue |
5 |
container_start_page |
053108 |
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1766331505381998592 |