A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting k-body fermionic embedded Gaussian ensembles


Por: Carro, Ernesto, Benet, Luis, Pérez Castillo I.

Publicada: 1 abr 2023
Resumen:
In spite of its simplicity, the central limit theorem captures one of the most outstanding phenomena in mathematical physics, that of universality. While this classical result is well understood, it is still not very clear what hap -pens to this universal behavior when the random variables become correlated. A fruitful mathematically laboratory to investigate the rising of new universal properties is offered by the set of eigenvalues of random matrices. In this regard, a lot of work has been done using the standard random matrix ensembles and focusing on the distribution of extreme eigenvalues. In this case, the distribution of the largest or smallest eigenvalue departs from the Fisher-Tippett-Gnedenko theorem yielding the celebrated Tracy-Widom distribution. One may wonder, yet again, how robust this new universal behavior captured by the Tracy-Widom distribution is when the correlation among eigenvalues changes. Few answers have been provided to this poignant question, and our intention in the present work is to contribute to this interesting unexplored territory. Thus, we study numerically the probability distribution for the normalized largest eigenvalue of the interacting k-body fermionic orthogonal and unitary embedded Gaussian ensembles in the diluted limit. We find a smooth transition from a slightly asymmetric Gaussian-like distribution, for small k/m, to the Tracy-Widom distribution as k/m ? 1, where k is the rank of the interaction and m is the number of fermions. Correlations at the edge of the spectrum are stronger for small values of k/m and are independent of the number of particles considered. Our results indicate that subtle correlations toward the edge of the spectrum distinguish the statistical properties of the spectrum of interacting many-body systems in the dilute limit, from those expected for the standard random matrix ensembles.

Filiaciones:
Carro, Ernesto:
 Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad s/n, Col. Chamilpa Morelos, Cuernavaca, CP 62210, Mexico

 Univ Nacl Autonoma Mexico, Inst Ciencias Fis, Ave Univ S-N, Cuernavaca 62210, Morelos, Mexico

Benet, Luis:
 Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Av. Universidad s/n, Col. Chamilpa Morelos, Cuernavaca, CP 62210, Mexico

 Univ Nacl Autonoma Mexico, Inst Ciencias Fis, Ave Univ S-N, Cuernavaca 62210, Morelos, Mexico

Pérez Castillo I.:
 Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Ciudad de Mexico, 09340, Mexico

Univ Autonoma Metropolitana Iztapalapa, Dept Fis, San Rafael Atlixco 186, Mexico City 09340, Mexico
ISSN: 17425468





JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Editorial
Institute of Physics Publishing, TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND, Reino Unido
Tipo de documento: Article
Volumen: 2023 Número: 4
Páginas:
WOS Id: 000964854700001
imagen Green Submitted, hybrid, Hybrid Gold

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