Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk

Akemann G, Gorski V, Kieburg M (2022)
Journal of Physics A: Mathematical and Theoretical 55(19): 194002.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little attention, where the density diverges or vanishes, respectively. This different behaviour is called hard or soft edge. We show that the spacings at the edges are almost indistinguishable from the spacing in the bulk of the spectrum. We present analytical results for consecutive spacings between the kth and (k + 1)st smallest eigenvalues in the chiral Gaussian unitary ensemble, both for finite- and large-n. The result depends on the number of the generic zero modes nu and the number of flavours N (f), which are given in terms of characteristic polynomials, as motivated by quantum chromodynamics (QCD). We find that the convergence in n is very rapid. The same can be said separately about the limit k -> infinity (limit to the bulk) and nu -> infinity (limit to the soft edge). Interestingly, the Wigner surmise is a very good approximation for all these cases and, apart from k = 1, shows a deviation below one percent. These findings are corroborated with Monte-Carlo simulations. We finally compare for k = 1 with data from QCD on the lattice, being in this symmetry class.
Stichworte
level spacing distribution; chiral Gaussian unitary ensemble; hard and; soft edge
Erscheinungsjahr
2022
Zeitschriftentitel
Journal of Physics A: Mathematical and Theoretical
Band
55
Ausgabe
19
Art.-Nr.
194002
ISSN
1751-8113
eISSN
1751-8121
Page URI
https://pub.uni-bielefeld.de/record/2962695

Zitieren

Akemann G, Gorski V, Kieburg M. Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk. Journal of Physics A: Mathematical and Theoretical . 2022;55(19): 194002.
Akemann, G., Gorski, V., & Kieburg, M. (2022). Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk. Journal of Physics A: Mathematical and Theoretical , 55(19), 194002. https://doi.org/10.1088/1751-8121/ac5f16
Akemann, G., Gorski, V., and Kieburg, M. (2022). Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk. Journal of Physics A: Mathematical and Theoretical 55:194002.
Akemann, G., Gorski, V., & Kieburg, M., 2022. Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk. Journal of Physics A: Mathematical and Theoretical , 55(19): 194002.
G. Akemann, V. Gorski, and M. Kieburg, “Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk”, Journal of Physics A: Mathematical and Theoretical , vol. 55, 2022, : 194002.
Akemann, G., Gorski, V., Kieburg, M.: Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk. Journal of Physics A: Mathematical and Theoretical . 55, : 194002 (2022).
Akemann, Gernot, Gorski, Valentin, and Kieburg, M. “Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk”. Journal of Physics A: Mathematical and Theoretical 55.19 (2022): 194002.
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2022-07-21T11:39:13Z
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arXiv: 2112.12447

Inspire: 1996513

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