The Jordan Wigner transformations and the fermionization of the XYZ spin Heisenberg chain. Algebra, geometry and physics?
We generalize our previous results for the (anisotropic) fermion XYZ Heisenberg chain; we avoid the free-fermion restriction. The departing point in the definition of two different Jordan Wigner transformations, significant for the Hamiltonians. Afterwards, with `their´ square roots we define four d...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | español |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71970 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/71970 |
| Access Level: | acceso abierto |
| Palabra clave: | 538.9 51-73 Time space Jordan Wigner Fermion XYZ chain Non free fermion Yang-Baxter Conserved quantities Elementary particles Física de materiales Física matemática Partículas 2208 Nucleónica |
| Sumario: | We generalize our previous results for the (anisotropic) fermion XYZ Heisenberg chain; we avoid the free-fermion restriction. The departing point in the definition of two different Jordan Wigner transformations, significant for the Hamiltonians. Afterwards, with `their´ square roots we define four different formulations of the local transition matrices with fermions. Due to our generalizations of the Yang-Baxter relation we observe a special role for the sign associated to the modulus k of the Jacobi elliptic functions. We define four Hamiltonians. We obtain the conserved quantities. Our construction and results suggest the importance of the geometry of the time and the space in various ways and a possible application to the elementary particles. |
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