### Quantum anisotropic sigma and lambda models as spin chains / Calan Appadu, Timothy Hollowood, Dafydd Price, Daniel Thompson

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

Swansea University Authors:

• PDF | Accepted Manuscript

12 month embargo.

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....
first_indexed 2018-08-22T15:35:53Z 2018-09-18T18:55:14Z cronfa43539 SURis 2018-09-18T12:59:26.4951072v2435392018-08-22Quantum anisotropic sigma and lambda models as spin chainsea9ca59fc948276ff2ab547e91bdf0c20000-0002-3258-320XTimothyHollowoodTimothy Hollowoodtruefalse9c8715ee44a574eda1194c9808d99c620000-0001-8319-8275DanielThompsonDaniel Thompsontruefalse2018-08-22SPHWe 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 ArticleJournal of Physics A: Mathematical and Theoretical5140405401Institute of Physics1751-81131751-812110920182018-09-1010.1088/1751-8121/aadc6dCOLLEGE NANMEPhysicsCOLLEGE CODESPHSwansea University2018-09-18T12:59:26.49510722018-08-22T14:10:47.1628130College of SciencePhysicsCalanAppadu1TimothyHollowood0000-0002-3258-320X2DafyddPrice3DanielThompson0000-0001-8319-827540043539-22082018141158.pdfSpinChainTBAMASTER.pdf2018-08-22T14:11:58.6900000Output393994application/pdfAccepted Manuscripttrue2019-08-23T00:00:00.000000012 month embargo.trueeng 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 College of Science 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 Quantum anisotropic sigma and lambda models as spin chains Quantum anisotropic sigma and lambda models as spin chains Timothy, Hollowood Daniel, Thompson Quantum anisotropic sigma and lambda models as spin chains Quantum anisotropic sigma and lambda models as spin chains Quantum anisotropic sigma and lambda models as spin chains Quantum anisotropic sigma and lambda models as spin chains Quantum anisotropic sigma and lambda models as spin chains ea9ca59fc948276ff2ab547e91bdf0c2 9c8715ee44a574eda1194c9808d99c62 ea9ca59fc948276ff2ab547e91bdf0c2_***_Timothy, Hollowood 9c8715ee44a574eda1194c9808d99c62_***_Daniel, Thompson Timothy, Hollowood Daniel, Thompson Calan Appadu Timothy Hollowood Dafydd Price Daniel Thompson Journal article Journal of Physics A: Mathematical and Theoretical 51 40 405401 2018 Swansea University 1751-8113 1751-8121 10.1088/1751-8121/aadc6d Institute of Physics College of Science collegeofscience College of Science collegeofscience College of Science Physics{{{_:::_}}}College of Science{{{_:::_}}}Physics 1 0 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. 2018-09-10T04:03:51Z 1712022441762488320 10.825742