Flat-band induced local Hilbert space fragmentation
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866912317751427072 |
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| author | Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Ahufinger, Verònica |
| author_facet | Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Ahufinger, Verònica |
| contents | We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states (CLSs) present in this class of flat-band lattices and the extended eigenstates of the system. In the presence of on-site bosonic interactions, such models exhibit a conserved quantity, the parity of the number of particles located in all the CLSs in a unit cell. As a consequence, the Hilbert space presents local fragmentation, which is only revealed upon rotating the basis of the Hamiltonian that decouples the CLSs at the single-particle level. We find that the fragmentation is strong and also robust to the addition of long-range interactions. As an example, we numerically analyze the fragmentation of the one-dimensional Pyrochlore chain, which exhibits both nonintegrable sectors, effective single-particle sectors, and frozen states. We also show that the entanglement entropies form a nested-dome structure typical of these fragmented systems and that thermalization is restricted to each sub-sector. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15660 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Flat-band induced local Hilbert space fragmentation Nicolau, Eloi Marques, Anselmo M. Dias, Ricardo G. Ahufinger, Verònica Statistical Mechanics Quantum Physics We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states (CLSs) present in this class of flat-band lattices and the extended eigenstates of the system. In the presence of on-site bosonic interactions, such models exhibit a conserved quantity, the parity of the number of particles located in all the CLSs in a unit cell. As a consequence, the Hilbert space presents local fragmentation, which is only revealed upon rotating the basis of the Hamiltonian that decouples the CLSs at the single-particle level. We find that the fragmentation is strong and also robust to the addition of long-range interactions. As an example, we numerically analyze the fragmentation of the one-dimensional Pyrochlore chain, which exhibits both nonintegrable sectors, effective single-particle sectors, and frozen states. We also show that the entanglement entropies form a nested-dome structure typical of these fragmented systems and that thermalization is restricted to each sub-sector. |
| title | Flat-band induced local Hilbert space fragmentation |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2306.15660 |