Study of quantum dimer and partition models on honeycomb lattices
The quantum dimer models (QDM's) have a series of interesting behaviors, such as topological order and spin liquid phases. In this thesis, we study these models for an honeycomb lattice, and also their equivalence with the partition problems, a subject of the domain of combinatorics. Firstly, w...
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ftsorbonneuniv:oai:HAL:tel-01191658v1 2023-06-11T04:09:27+02:00 Study of quantum dimer and partition models on honeycomb lattices Etude de modèles de dimères et partitions quantiques sur réseaux hexagonaux Milanetto Schlittler, Thiago Laboratoire de Physique Théorique de la Matière Condensée (LPTMC) Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS) Université Pierre et Marie Curie - Paris VI Rémy Mosseri 2015-06-15 https://theses.hal.science/tel-01191658 https://theses.hal.science/tel-01191658/document https://theses.hal.science/tel-01191658/file/these_archivage_3159461o.pdf en eng HAL CCSD NNT: 2015PA066120 tel-01191658 https://theses.hal.science/tel-01191658 https://theses.hal.science/tel-01191658/document https://theses.hal.science/tel-01191658/file/these_archivage_3159461o.pdf info:eu-repo/semantics/OpenAccess https://theses.hal.science/tel-01191658 Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066120⟩ Quantum dimer models Arctic circle Modèles de dimères quantiques Monte Carlo quantique Transitions de phase quantique Problèmes de partitions Déconfinement de Cantor Cercle arctique Croissance de cristaux [PHYS.PHYS]Physics [physics]/Physics [physics] info:eu-repo/semantics/doctoralThesis Theses 2015 ftsorbonneuniv 2023-05-30T00:38:20Z The quantum dimer models (QDM's) have a series of interesting behaviors, such as topological order and spin liquid phases. In this thesis, we study these models for an honeycomb lattice, and also their equivalence with the partition problems, a subject of the domain of combinatorics. Firstly, we study the RK model, for which the question on whenever one of its phases is gapped or not was still open. We describe an Monte-Carlo algorithm that allows to, among other results, access this gap directly. Secondly, we propose a generalization of this model. We find a more complex phase diagram, with phase transitions between the different topological sectors, and compatible with the Cantor deconfinement. Thirdly, we study the application of the RK model to honeycomb lattices associated to the planar partition problems. This imposes new boundary conditions, and we find a new model behavior. We also propose a méthod that uses the properties of the partition problem's configuration space to reduce the complexity of the QDM. Finally, we modelize the problems of classical crystal corner growth and melting with the formalism of the partition problems, finding a smooth transition between the limit interfaces of type "amoebae" and the arctic circle. Les modèles de dimères quantiques (QDM's) ont une série de comportements intéressants, comme de l'ordre topologique et des phases de liquides de spin. Dans cette thèse, nous explorons ces modèles pour un réseaux hexagonal, ainsi que leur équivalence aux problèmes de partitions, un sujet qui fait partie du domaine de la combinatoire. Premièrement, nous étudions le modèle RK, pour lequel la question sur la présence d'une phase avec un gap non-nul restait encore ouverte. Nous décrivons un algorithme Monte-Carlo qui nous permet, entre autres résultats, d'accéder directement au gap du système. Deuxièmement, nous proposons une généralisation de ce modèle. Nous trouvons un diagramme de phase beaucoup plus complexe, avec des transitions de phase entre différents secteurs topologiques, et ... Doctoral or Postdoctoral Thesis Arctic Arctique* HAL Sorbonne Université Arctic |
institution |
Open Polar |
collection |
HAL Sorbonne Université |
op_collection_id |
ftsorbonneuniv |
language |
English |
topic |
Quantum dimer models Arctic circle Modèles de dimères quantiques Monte Carlo quantique Transitions de phase quantique Problèmes de partitions Déconfinement de Cantor Cercle arctique Croissance de cristaux [PHYS.PHYS]Physics [physics]/Physics [physics] |
spellingShingle |
Quantum dimer models Arctic circle Modèles de dimères quantiques Monte Carlo quantique Transitions de phase quantique Problèmes de partitions Déconfinement de Cantor Cercle arctique Croissance de cristaux [PHYS.PHYS]Physics [physics]/Physics [physics] Milanetto Schlittler, Thiago Study of quantum dimer and partition models on honeycomb lattices |
topic_facet |
Quantum dimer models Arctic circle Modèles de dimères quantiques Monte Carlo quantique Transitions de phase quantique Problèmes de partitions Déconfinement de Cantor Cercle arctique Croissance de cristaux [PHYS.PHYS]Physics [physics]/Physics [physics] |
description |
The quantum dimer models (QDM's) have a series of interesting behaviors, such as topological order and spin liquid phases. In this thesis, we study these models for an honeycomb lattice, and also their equivalence with the partition problems, a subject of the domain of combinatorics. Firstly, we study the RK model, for which the question on whenever one of its phases is gapped or not was still open. We describe an Monte-Carlo algorithm that allows to, among other results, access this gap directly. Secondly, we propose a generalization of this model. We find a more complex phase diagram, with phase transitions between the different topological sectors, and compatible with the Cantor deconfinement. Thirdly, we study the application of the RK model to honeycomb lattices associated to the planar partition problems. This imposes new boundary conditions, and we find a new model behavior. We also propose a méthod that uses the properties of the partition problem's configuration space to reduce the complexity of the QDM. Finally, we modelize the problems of classical crystal corner growth and melting with the formalism of the partition problems, finding a smooth transition between the limit interfaces of type "amoebae" and the arctic circle. Les modèles de dimères quantiques (QDM's) ont une série de comportements intéressants, comme de l'ordre topologique et des phases de liquides de spin. Dans cette thèse, nous explorons ces modèles pour un réseaux hexagonal, ainsi que leur équivalence aux problèmes de partitions, un sujet qui fait partie du domaine de la combinatoire. Premièrement, nous étudions le modèle RK, pour lequel la question sur la présence d'une phase avec un gap non-nul restait encore ouverte. Nous décrivons un algorithme Monte-Carlo qui nous permet, entre autres résultats, d'accéder directement au gap du système. Deuxièmement, nous proposons une généralisation de ce modèle. Nous trouvons un diagramme de phase beaucoup plus complexe, avec des transitions de phase entre différents secteurs topologiques, et ... |
author2 |
Laboratoire de Physique Théorique de la Matière Condensée (LPTMC) Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS) Université Pierre et Marie Curie - Paris VI Rémy Mosseri |
format |
Doctoral or Postdoctoral Thesis |
author |
Milanetto Schlittler, Thiago |
author_facet |
Milanetto Schlittler, Thiago |
author_sort |
Milanetto Schlittler, Thiago |
title |
Study of quantum dimer and partition models on honeycomb lattices |
title_short |
Study of quantum dimer and partition models on honeycomb lattices |
title_full |
Study of quantum dimer and partition models on honeycomb lattices |
title_fullStr |
Study of quantum dimer and partition models on honeycomb lattices |
title_full_unstemmed |
Study of quantum dimer and partition models on honeycomb lattices |
title_sort |
study of quantum dimer and partition models on honeycomb lattices |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://theses.hal.science/tel-01191658 https://theses.hal.science/tel-01191658/document https://theses.hal.science/tel-01191658/file/these_archivage_3159461o.pdf |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic Arctique* |
genre_facet |
Arctic Arctique* |
op_source |
https://theses.hal.science/tel-01191658 Physics [physics]. Université Pierre et Marie Curie - Paris VI, 2015. English. ⟨NNT : 2015PA066120⟩ |
op_relation |
NNT: 2015PA066120 tel-01191658 https://theses.hal.science/tel-01191658 https://theses.hal.science/tel-01191658/document https://theses.hal.science/tel-01191658/file/these_archivage_3159461o.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1768383321351389184 |