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Quantum anisotropic sigma and lambda models as spin chains

Calan Appadu, Timothy Hollowood Orcid Logo, Dafydd Price, Daniel Thompson Orcid Logo

Journal of Physics A: Mathematical and Theoretical, Volume: 51, Issue: 40, Start page: 405401

Swansea University Authors: Timothy Hollowood Orcid Logo, Daniel Thompson Orcid Logo

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DOI (Published version): 10.1088/1751-8121/aadc6d

Abstract

We consider lambda and anisotropic deformations of the $\SU(2)$ principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ Heisenberg chain and can be solved by using the Bethe Ansatz....

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Published in: Journal of Physics A: Mathematical and Theoretical
ISSN: 1751-8113 1751-8121
Published: Institute of Physics 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa43539
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first_indexed 2018-08-22T15:35:53Z
last_indexed 2018-09-18T18:55:14Z
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spelling 2018-09-18T12:59:26.4951072 v2 43539 2018-08-22 Quantum anisotropic sigma and lambda models as spin chains ea9ca59fc948276ff2ab547e91bdf0c2 0000-0002-3258-320X Timothy Hollowood Timothy Hollowood true false 9c8715ee44a574eda1194c9808d99c62 0000-0001-8319-8275 Daniel Thompson Daniel Thompson true false 2018-08-22 SPH We consider lambda and anisotropic deformations of the $\SU(2)$ principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ Heisenberg chain and can be solved by using the Bethe Ansatz. This yields the spectrum and S-matrix of the excitations. In particular, we find the S-matrix in the gapped anti-ferromagnetic regime. In this regime, a continuum limit does not exist and this suggests that the field theories in this regime, precisely ones with a cyclic RG like the Yang-Baxter deformations, may only exist as effective theories. In a certain limit, we show that the XXZ type lambda model gives the symmetric space $\SU(2)/\U(1)$ lambda model and, hence, we are able to find its spectrum and S-matrix and show that it gives the S-matrix of the $\text{O}(3)$ sigma model in the appropriate limit. Finally, we show the full consistency of the S-matrix and the Lagrangian formulations of the lambda model, by coupling to a conserved charge and computing the way the ground state energy changes in both pictures. Journal Article Journal of Physics A: Mathematical and Theoretical 51 40 405401 Institute of Physics 1751-8113 1751-8121 10 9 2018 2018-09-10 10.1088/1751-8121/aadc6d COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2018-09-18T12:59:26.4951072 2018-08-22T14:10:47.1628130 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Calan Appadu 1 Timothy Hollowood 0000-0002-3258-320X 2 Dafydd Price 3 Daniel Thompson 0000-0001-8319-8275 4 0043539-22082018141158.pdf SpinChainTBAMASTER.pdf 2018-08-22T14:11:58.6900000 Output 393994 application/pdf Accepted Manuscript true 2019-08-23T00:00:00.0000000 12 month embargo. true eng
title Quantum anisotropic sigma and lambda models as spin chains
spellingShingle Quantum anisotropic sigma and lambda models as spin chains
Timothy Hollowood
Daniel Thompson
title_short Quantum anisotropic sigma and lambda models as spin chains
title_full Quantum anisotropic sigma and lambda models as spin chains
title_fullStr Quantum anisotropic sigma and lambda models as spin chains
title_full_unstemmed Quantum anisotropic sigma and lambda models as spin chains
title_sort Quantum anisotropic sigma and lambda models as spin chains
author_id_str_mv ea9ca59fc948276ff2ab547e91bdf0c2
9c8715ee44a574eda1194c9808d99c62
author_id_fullname_str_mv ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy Hollowood
9c8715ee44a574eda1194c9808d99c62_***_Daniel Thompson
author Timothy Hollowood
Daniel Thompson
author2 Calan Appadu
Timothy Hollowood
Dafydd Price
Daniel Thompson
format Journal article
container_title Journal of Physics A: Mathematical and Theoretical
container_volume 51
container_issue 40
container_start_page 405401
publishDate 2018
institution Swansea University
issn 1751-8113
1751-8121
doi_str_mv 10.1088/1751-8121/aadc6d
publisher Institute of Physics
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 Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description We consider lambda and anisotropic deformations of the $\SU(2)$ principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ Heisenberg chain and can be solved by using the Bethe Ansatz. This yields the spectrum and S-matrix of the excitations. In particular, we find the S-matrix in the gapped anti-ferromagnetic regime. In this regime, a continuum limit does not exist and this suggests that the field theories in this regime, precisely ones with a cyclic RG like the Yang-Baxter deformations, may only exist as effective theories. In a certain limit, we show that the XXZ type lambda model gives the symmetric space $\SU(2)/\U(1)$ lambda model and, hence, we are able to find its spectrum and S-matrix and show that it gives the S-matrix of the $\text{O}(3)$ sigma model in the appropriate limit. Finally, we show the full consistency of the S-matrix and the Lagrangian formulations of the lambda model, by coupling to a conserved charge and computing the way the ground state energy changes in both pictures.
published_date 2018-09-10T03:54:46Z
_version_ 1763752737533591552
score 10.99807

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