Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
We solve in closed form the simplest (su(1 vertical bar 1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/34701 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/34701 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Inverse-square exchange Haldane-shastry type Heisenberg chain Yangian symmetry Exact spectrum Systems Models Gas Física-Modelos matemáticos Física matemática |
| Sumario: | We solve in closed form the simplest (su(1 vertical bar 1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1 vertical bar 1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane-Shastry chain. |
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