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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Detalles Bibliográficos
Autor: Olmedilla Moreno, Eugenio
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
Descripción
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.