Journal article 1644 views 187 downloads
Quantum anisotropic sigma and lambda models as spin chains
Calan Appadu,
Timothy Hollowood 
,
Dafydd Price,
Daniel Thompson
,
Dafydd Price,
Daniel Thompson
Journal of Physics A: Mathematical and Theoretical, Volume: 51, Issue: 40, Start page: 405401
Swansea University Authors:
Timothy Hollowood , Daniel Thompson
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....
| Published in: | Journal of Physics A: Mathematical and Theoretical |
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| ISSN: | 1751-8113 1751-8121 |
| Published: |
Institute of Physics
2018
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa43539 |
| 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. |
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| College: |
Faculty of Science and Engineering |
| Issue: |
40 |
| Start Page: |
405401 |