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Artículo

Quasi-exact solvability and entropies of the one dimensional regularised Calogero model

Pont, Federico ManuelIcon ; Osenda, OmarIcon ; Serra, PabloIcon
Fecha de publicación: 17/04/2018
Editorial: IOP Publishing
Revista: Journal of Physics A: Mathematical and Theoretical
ISSN: 1751-8113
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Otras Ciencias Físicas

Resumen

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun's confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.
Palabras clave: ENTANGLEMENT SPECTRUM , INTERACTING PARTICLES IN ONE DIMENSION , NUMERICAL METHODS FOR ONE-BODY ORBITALS , QUASI-EXACTLY SOLVABLE HAMILTONIANS
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution 2.5 Unported (CC BY 2.5)
Identificadores
URI: http://hdl.handle.net/11336/91693
URL: http://iopscience.iop.org/article/10.1088/1751-8121/aab85e
DOI: http://dx.doi.org/10.1088/1751-8121/aab85e
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Articulos(IFEG)
Articulos de INST.DE FISICA ENRIQUE GAVIOLA
Citación
Pont, Federico Manuel; Osenda, Omar; Serra, Pablo; Quasi-exact solvability and entropies of the one dimensional regularised Calogero model; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 51; 19; 17-4-2018; 1-24
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