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

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 $π$-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.

💡 Research Summary

In this work the authors explore the spectral statistics of an interacting fermionic model obtained by projecting the Hubbard interaction onto the two lowest‑energy flat bands of the dice lattice threaded by a π‑flux. The dice lattice hosts two perfectly flat bands whose Wannier functions are compactly localized, allowing the interaction to be expressed as a finite set of short‑range terms after projection. The resulting effective Hamiltonian can be written as

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