Information Dynamics in a Model with Hilbert Space Fragmentation

TL;DR

This paper investigates the non-equilibrium dynamics of a frustrated spin ladder model, revealing how Hilbert space fragmentation leads to anomalous entanglement revivals and complex information spreading behaviors.

Contribution

It demonstrates that Hilbert space fragmentation causes persistent entanglement revivals and local thermalization within fragments, advancing understanding of non-integrable quantum systems.

Findings

Entanglement entropy shows non-damped revivals due to fragmentation.

Eigenstate thermalization occurs within large Hilbert space fragments.

OTOC exhibits short-distance oscillations and sub-ballistic spreading.

Abstract

The fully frustrated ladder - a quasi-1D geometrically frustrated spin one half Heisenberg model - is non-integrable with local conserved quantities on rungs of the ladder, inducing the fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets and whose persistence is therefore a consequence of fragmentation. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.