Modular invariance in the gapped XYZ spin-1/2 chain
We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase diagram of the model, which is composed of 12 adjacent regions, related to one another by a spin rotation. This ext...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88718 |
| _version_ | 1826192826722942976 |
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| author | Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco |
| author_sort | Ercolessi, Elisa |
| collection | MIT |
| description | We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase diagram of the model, which is composed of 12 adjacent regions, related to one another by a spin rotation. This extension is based on the modular properties of the elliptic functions and we show how rotations in parameter space correspond to the double covering PGL(2,Z) of the modular group, implying that the partition function of the XYZ chain is invariant under this group in parameter space, in the same way as a conformal field theory partition function is invariant under the modular group acting in real space. The encoding of the symmetries of the model into the modular properties of the partition function could shed light on the general structure of integrable models. |
| first_indexed | 2024-09-23T09:29:47Z |
| format | Article |
| id | mit-1721.1/88718 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:29:47Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/887182022-09-26T11:46:14Z Modular invariance in the gapped XYZ spin-1/2 chain Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco Massachusetts Institute of Technology. Department of Physics Franchini, Fabio We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase diagram of the model, which is composed of 12 adjacent regions, related to one another by a spin rotation. This extension is based on the modular properties of the elliptic functions and we show how rotations in parameter space correspond to the double covering PGL(2,Z) of the modular group, implying that the partition function of the XYZ chain is invariant under this group in parameter space, in the same way as a conformal field theory partition function is invariant under the modular group acting in real space. The encoding of the symmetries of the model into the modular properties of the partition function could shed light on the general structure of integrable models. 2014-08-15T16:12:00Z 2014-08-15T16:12:00Z 2013-09 2013-08 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88718 Ercolessi, Elisa, Stefano Evangelisti, Fabio Franchini, and Francesco Ravanini. "Modular invariance in the gapped XYZ spin-1/2 chain." Phys. Rev. B 88, 104418 (September 2013). © 2013 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevB.88.104418 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society American Physical Society |
| spellingShingle | Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco Modular invariance in the gapped XYZ spin-1/2 chain |
| title | Modular invariance in the gapped XYZ spin-1/2 chain |
| title_full | Modular invariance in the gapped XYZ spin-1/2 chain |
| title_fullStr | Modular invariance in the gapped XYZ spin-1/2 chain |
| title_full_unstemmed | Modular invariance in the gapped XYZ spin-1/2 chain |
| title_short | Modular invariance in the gapped XYZ spin-1/2 chain |
| title_sort | modular invariance in the gapped xyz spin 1 2 chain |
| url | http://hdl.handle.net/1721.1/88718 |
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