Robust Hilbert space fragmentation in group-valued loop models
arXiv:2406.19386 · doi:10.1103/PhysRevB.111.024310
Abstract
We introduce a large class of models exhibiting robust ergodicity breaking in quantum dynamics. Our work is inspired by recent discussions of "topologically robust Hilbert space fragmentation," but massively generalizes in two directions: firstly from states describable as "loop-soups" to a broader class of states reminiscent of string-nets and sponges, and secondly from models restricted to square or cubic lattices, to models defined on arbitrary lattices (and even arbitrary graphs without translation invariance). Our constructions leverage a recently proposed group-theory framework [PRX 14, 021034 (2024)], and identify a host of new phenomena arising from the interplay of "group-model dynamics" and lattice structure. We make crisp connections to gauge theories, and our construction generalizes Kitaev's quantum double to infinite groups.
26 pages, 10 figures
References in corpus (28)
- Fault-tolerant quantum computation by anyons
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Many-body localization, thermalization, and entanglement
- Generalized Global Symmetries
- On Many-Body Localization for Quantum Spin Chains
- Localization from Hilbert space shattering: from theory to physical realizations
- Local constraints can globally shatter Hilbert space: a new route to quantum information protection
- Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
- Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
- Stability and instability towards delocalization in MBL systems
- Generalized Symmetries in Condensed Matter
- A symmetry principle for Topological Quantum Order
- A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Quantum Many-Body Scars: A Quasiparticle Perspective
- Topological order in a 3D toric code at finite temperature
- Localization in fractonic random circuits
- Quaternion, harmonic oscillator, and high-dimensional topological states
- Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
- Ergodicity breaking provably robust to arbitrary perturbations
- Prethermalization and the local robustness of gapped systems
- Topologically stable ergodicity breaking from emergent higher-form symmetries in generalized quantum loop models
- Eigenstate localization in a many-body quantum system
- Glassy word problems: ultraslow relaxation, Hilbert space jamming, and computational complexity
- On the Cleaning Lemma of Quantum Coding Theory
- Bicolor loop models and their long range entanglement