Flat-band induced local Hilbert space fragmentation

TL;DR

This paper shows that flat-band lattices with local symmetries have a fragmented Hilbert space, leading to constrained thermalization and robust local conservation laws, demonstrated through theoretical analysis and numerical examples.

Contribution

It introduces a new class of flat-band lattices with local Hilbert space fragmentation due to commutative local symmetries and equitable partition theorem.

Findings

Hilbert space fragmentation is robust to long-range interactions.

Entanglement entropy exhibits a nested-dome structure.

Thermalization is restricted within sub-sectors.

Abstract

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.