Arrested Development and Fragmentation in Strongly-Interacting Floquet Systems

TL;DR

This paper investigates how interactions in strongly-interacting Floquet systems can lead to classical-like dynamics, Hilbert space fragmentation, and complex entanglement structures, depending on specific parameter conditions.

Contribution

It introduces conditions based on Diophantine equations under which Floquet evolution acts as a permutation or causes fragmentation of the Hilbert space.

Findings

Certain parameter values enable permutation-like evolution.

Partial satisfaction of conditions leads to Hilbert space fragmentation.

Fragmented states exhibit high entanglement and level repulsion.

Abstract

We explore how interactions can facilitate classical like dynamics in models with sequentially activated hopping. Specifically, we add local and short range interaction terms to the Hamiltonian, and ask for conditions ensuring the evolution acts as a permutation on initial local number Fock states. We show that at certain values of hopping and interactions, determined by a set of Diophantine equations, such evolution can be realized. When only a subset of the Diophantine equations is satisfied the Hilbert space can be fragmented into frozen states, states obeying cellular automata like evolution and subspaces where evolution mixes Fock states and is associated with eigenstates exhibiting high entanglement entropy and level repulsion.