Parity-dependent double degeneracy and spectral statistics in the projected dice lattice
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915794396381184 |
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| author | Swaminathan, Koushik Moustaj, Anouar Lado, Jose L. Peotta, Sebastiano |
| author_facet | Swaminathan, Koushik Moustaj, Anouar Lado, Jose L. Peotta, Sebastiano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11844 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parity-dependent double degeneracy and spectral statistics in the projected dice lattice Swaminathan, Koushik Moustaj, Anouar Lado, Jose L. Peotta, Sebastiano Strongly Correlated Electrons Mathematical Physics Quantum Physics 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. |
| title | Parity-dependent double degeneracy and spectral statistics in the projected dice lattice |
| topic | Strongly Correlated Electrons Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2602.11844 |