Hilbert space fragmentation in driven-dephasing Rydberg atom array

TL;DR

This paper explores how Hilbert space fragmentation occurs in driven-dephasing Rydberg atom chains, revealing the underlying symmetries, zero modes, and exponential growth of fragmented states, with implications for controlling many-body quantum dynamics.

Contribution

It demonstrates the fundamental link between Hilbert space fragmentation and metastable states in driven-dephasing Rydberg systems, identifying the symmetry and zero modes responsible for fragmentation.

Findings

HSF leads to multiple long-lived metastable states.

Number of fragmented states grows exponentially with chain length.

Identifies symmetry and zero modes underlying HSF.

Abstract

We investigate the onset and mechanism of Hilbert space fragmentation (HSF) in a chain of strongly interacting Rydberg atoms subject to local dephasing. It is found that the emergence of multiple long-lived metastable states is fundamentally tied to HSF of the driven-dephasing Rydberg atom system. We demonstrate that the manifesting HSF is captured by a dephasing PXP model that supports multiple degenerate zero modes. These modes form disconnected, block-diagonal subspaces of maximally mixed states, which consist of many-body spin states sharing the same symmetry. A key result is the identification of the underlying symmetry in the HSF, where conserved quantities in each subspace are defined by the consecutive double excitation addressing operator. Moreover, we show explicitly that the number of the fragmented Hilbert space grows exponentially with the chain length, following a modified Fibonacci sequence. Our work provides insights into many-body dynamics under dynamical constraints and opens avenues for controlling and manipulating HSF in Rydberg atom systems.