Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models

Abstract

We present a set of generalized quantum loop models which provably exhibit topologically stable ergodicity breaking. These results hold for both periodic and open boundary conditions, and derive from a one-form symmetry (notably not being restricted to sectors of extremal one-form charge). We identify simple models in which this one-form symmetry can be emergent, giving rise to the aforementioned ergodicity breaking as an exponentially long-lived prethermal phenomenon. We unveil a web of dualities that connects these models, in certain limits, to models that have previously been discussed in the literature. We also identify nonlocal conserved quantities in such models that correspond to a pattern of system-spanning domain walls, and which are robust to the addition of arbitrary $k$-local perturbations.

22+8 pages, 8 figures; v2 includes minor revisions and additional references

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• Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity
• Theory of metastable states in many-body quantum systems
• Towards absolutely stable ergodicity breaking in two and three dimensions
• Robust Hilbert space fragmentation in group-valued loop models
• Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries
• Dynamics in the presence of local symmetry-breaking impurities
• Obstruction to Ergodicity from Locality and $U(1)$ Higher Symmetries on the Lattice