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A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model

Mark Kelbert, Yurii Suhov

Advances in Mathematical Physics, Volume: 2013, Pages: 1 - 20

Swansea University Author: Mark Kelbert

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DOI (Published version): 10.1155/2013/637375

Abstract

This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on bi-dimensional graphs where particles can jump from a vertex to another...

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Published in: Advances in Mathematical Physics
ISSN: 1687-9120
Published: 2013
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URI: https://cronfa.swan.ac.uk/Record/cronfa14984
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first_indexed 2013-07-23T12:13:36Z
last_indexed 2018-02-09T04:46:39Z
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spelling 2013-11-05T15:12:04.7410218 v2 14984 2013-06-03 A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model 3a81821a33f0e13488bd6a81cdc30f9d Mark Kelbert Mark Kelbert true false 2013-06-03 FGSEN This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on bi-dimensional graphs where particles can jump from a vertex to another (a generalized Hubbard model). The Feynman--Kac representation is used for proving that if the local Hamiltonians are invariant under a continuous group of transformations ${\tt G}$ (a Euclidean space or a torus of dimension $d'$ acting on a torus of dimension $d\geq d'$) then any infinite-volume Gibbs state from a certain class (introduced in the paper) is also ${\tt G}$-invariant. Journal Article Advances in Mathematical Physics 2013 1 20 1687-9120 31 12 2013 2013-12-31 10.1155/2013/637375 http://uk.arxiv.org/abs/1210.8344v3 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2013-11-05T15:12:04.7410218 2013-06-03T10:16:27.4978962 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Mark Kelbert 1 Yurii Suhov 2
title A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
spellingShingle A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
Mark Kelbert
title_short A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
title_full A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
title_fullStr A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
title_full_unstemmed A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
title_sort A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model
author_id_str_mv 3a81821a33f0e13488bd6a81cdc30f9d
author_id_fullname_str_mv 3a81821a33f0e13488bd6a81cdc30f9d_***_Mark Kelbert
author Mark Kelbert
author2 Mark Kelbert
Yurii Suhov
format Journal article
container_title Advances in Mathematical Physics
container_volume 2013
container_start_page 1
publishDate 2013
institution Swansea University
issn 1687-9120
doi_str_mv 10.1155/2013/637375
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://uk.arxiv.org/abs/1210.8344v3
document_store_str 0
active_str 0
description This paper is the second in a series of papers considering symmetry properties of a bosonic quantum system over an 2D graph, with continuous spins, in the spirit of the Mermin--Wagner theorem. Here we consider bosonic systems on bi-dimensional graphs where particles can jump from a vertex to another (a generalized Hubbard model). The Feynman--Kac representation is used for proving that if the local Hamiltonians are invariant under a continuous group of transformations ${\tt G}$ (a Euclidean space or a torus of dimension $d'$ acting on a torus of dimension $d\geq d'$) then any infinite-volume Gibbs state from a certain class (introduced in the paper) is also ${\tt G}$-invariant.
published_date 2013-12-31T03:17:06Z
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score 11.012857

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