Flat-band induced local Hilbert space fragmentation

Fuente: arXiv
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Autori principali: Nicolau, Eloi, Marques, Anselmo M., Dias, Ricardo G., Ahufinger, Verònica
Natura: Preprint
Pubblicazione: 2023
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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