Year: 2022
Type: preprint
Abstract: Models with Hilbert space fragmentation are characterized by (exponentially) many dynamically disconnected subspaces, not associated with conventional symmetries but captured by nontrivial Krylov subspaces. These subspaces usually exhibit a whole range of thermalization properties, from chaotic to integrable, to quantum many-body scars. However, so far, they have not been properly defined, nor can they be easily found, given a Hamiltonian. In this work, we consider Hamiltonians that have integer representations, a common feature of many (most) celebrated models in condensed matter. We show the equivalence of the integer characteristic polynomial factorization and the existence of Krylov subspaces generated from integer vectors. Considering the pair-hopping model, we illustrate how the factorization property can be used as a method to unveil Hilbert space fragmentation. We discuss the generalization over other rings of integers, for example those based on the cyclotomic field which are relevant when working in a given ($\ne 0, π$) momentum sector.
Authors: Regnault, Nicolas, Liu, Shuo, Bernevig, B. Andrei
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: NEW TOPOLOGICAL FRONTIER
OpenAlex ID: W4306814867