Universal transition of spectral fluctuation in particle-hole symmetric
system
- URL: http://arxiv.org/abs/2207.14665v2
- Date: Wed, 9 Aug 2023 09:52:20 GMT
- Title: Universal transition of spectral fluctuation in particle-hole symmetric
system
- Authors: Triparna Mondal and Shashi C. L. Srivastava
- Abstract summary: We study the spectral properties of a system with particle-hole symmetry in random matrix setting.
We observe a crossover from Poisson to Wigner-Dyson like behavior in average local ratio of spacing within a spectrum of single matrix.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We study the spectral properties of a multiparametric system having
particle-hole symmetry in random matrix setting. We observe a crossover from
Poisson to Wigner-Dyson like behavior in average local ratio of spacing within
a spectrum of single matrix as a function of effective single parameter
referred to as complexity parameter. The average local ratio of spacing varies
logarithmically in complexity parameter across the transition. This behavior is
universal for different ensembles subjected to same matrix constraint like
particle-hole symmetry. The universality of this dependence is further
established by studying interpolating ensemble connecting systems with
particle-hole symmetry to that with chiral symmetry. For each interpolating
ensemble the behavior remains logarithmic in complexity parameter. We verify
this universality of spectral fluctuation in case of a 2D Su-Schrieffer-Heeger
(SSH) like model along with the logarithmic dependence on complexity parameter
for ratio of spacing during transition from integrable to non-integrable limit.
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