Universal transition of spectral fluctuation in particle-hole symmetric system

TL;DR

This paper investigates how spectral fluctuations in particle-hole symmetric systems transition from Poisson to Wigner-Dyson behavior, revealing a universal logarithmic dependence on a complexity parameter across different models and ensembles.

Contribution

It demonstrates the universal logarithmic transition of spectral fluctuations in particle-hole symmetric systems and connects random matrix results with a 2D SSH-like model.

Findings

Spectral ratio of spacing transitions logarithmically with complexity parameter.

Universality of this transition across different ensembles and symmetries.

Verification in a 2D SSH-like model confirms the theoretical predictions.

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.