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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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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. 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.
College: Faculty of Science and Engineering
Issue: 40
Start Page: 405401

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