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 circlephenomenon, namely a spatial phase separation between a cri...
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ftunifrgnorteir:oai:https://repositorio.ufrn.br:123456789/30335 2023-05-15T14:27:09+02:00 Inhomogeneous field theory inside the arctic circle Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo 2016-05-19 application/pdf https://repositorio.ufrn.br/handle/123456789/30335 https://doi.org/10.1088/1742-5468/2016/05/053108 en eng IOP Publishing ALLEGRA, Nicolas; DUBAIL, Jérôme; STÉPHAN, Jean-Marie; VITI, Jacopo. Inhomogeneous field theory inside the arctic circle. Journal Of Statistical Mechanics: Theory and Experiment, [S.L.], v. 2016, n. 5, p. 053108, 19 maio 2016. Disponível em: https://iopscience.iop.org/article/10.1088/1742-5468/2016/05/053108. Acesso em: 18 ago. 2020. http://dx.doi.org/10.1088/1742-5468/2016/05/053108 1742-5468 https://repositorio.ufrn.br/handle/123456789/30335 doi:10.1088/1742-5468/2016/05/053108 Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ CC-BY Conformal field theory Integrable spin chains (vertex models) Quantum quenches article 2016 ftunifrgnorteir https://doi.org/10.1088/1742-5468/2016/05/053108 2021-12-19T17:59:19Z 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 circlephenomenon, 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)twodimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac 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 (∆=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 Arctic Universidade Federal do Rio Grande do Norte: Repositório Institucional (RI UFRN) Arctic Journal of Statistical Mechanics: Theory and Experiment 2016 5 053108 |
institution |
Open Polar |
collection |
Universidade Federal do Rio Grande do Norte: Repositório Institucional (RI UFRN) |
op_collection_id |
ftunifrgnorteir |
language |
English |
topic |
Conformal field theory Integrable spin chains (vertex models) Quantum quenches |
spellingShingle |
Conformal field theory Integrable spin chains (vertex models) Quantum quenches Allegra, Nicolas Dubail, Jérôme Stéphan, Jean-Marie Viti, Jacopo Inhomogeneous field theory inside the arctic circle |
topic_facet |
Conformal field theory Integrable spin chains (vertex models) Quantum quenches |
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 circlephenomenon, 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)twodimensional massless Dirac field theory. It is observed that this theory is inhomogenous: the metric is position-dependent, so it is in fact a Dirac 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 (∆=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 |
format |
Article in Journal/Newspaper |
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 |
IOP Publishing |
publishDate |
2016 |
url |
https://repositorio.ufrn.br/handle/123456789/30335 https://doi.org/10.1088/1742-5468/2016/05/053108 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Arctic |
genre_facet |
Arctic Arctic |
op_relation |
ALLEGRA, Nicolas; DUBAIL, Jérôme; STÉPHAN, Jean-Marie; VITI, Jacopo. Inhomogeneous field theory inside the arctic circle. Journal Of Statistical Mechanics: Theory and Experiment, [S.L.], v. 2016, n. 5, p. 053108, 19 maio 2016. Disponível em: https://iopscience.iop.org/article/10.1088/1742-5468/2016/05/053108. Acesso em: 18 ago. 2020. http://dx.doi.org/10.1088/1742-5468/2016/05/053108 1742-5468 https://repositorio.ufrn.br/handle/123456789/30335 doi:10.1088/1742-5468/2016/05/053108 |
op_rights |
Attribution 3.0 Brazil http://creativecommons.org/licenses/by/3.0/br/ |
op_rightsnorm |
CC-BY |
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 |
_version_ |
1766300749187252224 |