Parity-dependent double degeneracy and spectral statistics in the projected dice lattice

TL;DR

This paper studies the spectral statistics of a fermionic system on the dice lattice with flux, revealing parity-dependent random matrix ensemble behaviors and an unprecedented coexistence of two ensembles in one system.

Contribution

It uncovers parity-dependent spectral statistics and the coexistence of Gaussian Orthogonal and Unitary Ensembles in a single flat-band fermionic system.

Findings

Even particle number spectra follow GOE statistics.

Odd particle number spectra exhibit double degeneracy and GUE statistics.

The coexistence of two different random matrix ensembles in one system is demonstrated.

Abstract

We investigate the spectral statistics of an interacting fermionic system derived by projecting the Hubbard interaction onto the two lowest-energy, degenerate flat bands of the dice lattice subjected to a $\pi$-flux. Surprisingly, the distributions of level spacings and gap ratios correspond to distinct Gaussian ensembles, depending on the parity of the particle number. For an even number of particles, the spectra conform to the Gaussian Orthogonal Ensemble, as expected for a time-reversal-symmetric Hamiltonian. In stark contrast, the odd-parity sector exhibits exact double degeneracy of all eigenstates even after resolving all known symmetries, and the Gaussian Unitary Ensemble accurately describes the spacing distribution between these doublets. The simultaneous emergence of two different random-matrix ensembles within a single physical system constitutes an unprecedented finding, opening new avenues for both random matrix theory and flat-band physics.