Hierarchy of degenerate stationary states in a boundary-driven dipole-conserving spin chain

TL;DR

This paper reveals how boundary-driven dipole-conserving spin chains exhibit a hierarchy of degenerate steady states, enabling stabilization of quantum information-preserving states and suppression of current, highlighting ergodicity breaking in open quantum systems.

Contribution

It introduces a hierarchy of degenerate steady states in boundary-driven dipole-conserving spin chains, demonstrating control over ergodicity breaking and information preservation.

Findings

Existence of a hierarchy of degenerate steady states.

Ability to stabilize mixed states and decoherence-free subspaces.

Suppression of current due to dipole conservation.

Abstract

Kinetically constrained spin chains serve as a prototype for structured ergodicity breaking in isolated quantum systems. We show that such a system exhibits a hierarchy of degenerate steady states when driven by incoherent pump and loss at the boundary. By tuning the relative pump and loss and how local the constraints are, one can stabilize mixed steady states, noiseless subsystems, and various decoherence-free subspaces, all of which preserve large amounts of information. We also find that a dipole-conserving bulk suppresses current in steady state. These exact results based on the flow in Hilbert space hold regardless of the specific Hamiltonian or drive mechanism. Our findings show that a competition of kinetic constraints and local drives can induce different forms of ergodicity breaking in open systems, which should be accessible in quantum simulators.