Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
By Pablo Sala, Tibor Rakovszky, R. Verresen, Michael Jason Knap, Frank Pollmann. Physical Review X, 2019
466 citations recorded by the source corpus.
We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total $S^z$) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value---showcasing non-thermal behavior. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local $S^z$ basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment conserving random unitary circuit models for which we reach identical conclusions.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/6e99c5e247c59822a8b991e35e3e99d0a4ab3474
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Fracton phases of matter (2020, background): “Meanwhile, Reference [108] proposed a more microscopic picture for this localization in terms of “fragmentation” of the Hilbert space, which implies the presence of “inert” localized states with trivial time evolution.”
- Quantum many-body scars and weak breaking of ergodicity (2020, methodology): “The model of the fractional quantum Hall effect on a thin cylinder [48] supports scarred eigenstates and revivals from a product state (c), while local observables in a spin-1 model with dipole conservation symmetry [49] weakly violate the ETH (d).”
- Fracton hydrodynamics (2020, background): “edu While local mobility constraints can lead to very long relaxation times for equilibration [46] and can even produce localization in certain subspaces [47–49], typical initial states in most fracton systems can reach local equilibrium.”
- Hilbert Space Fragmentation and Commutant Algebras (2021, methodology): “VI, we discuss the well-known strongly-fragmented spin-1 dipole-conserving model [27, 43] in the commutant algebra language, and we analytically construct and count the full commutant.”
- Statistical localization: From strong fragmentation to strong edge modes (2019, background): “relations) occuring in the bulk, which was observed previously [50].”
- Random Quantum Circuits (2022, background): “This was found to lead to a novel form of ergodicity breaking via the “shattering” of Hilbert space into exponentially many dynamically decoupled sectors, with no dynamical path even between states with the same charge and dipole quantum numbers (192, 193) — a surprising result in light of the conve”
- Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “A further distinction between strong and weak fragmentation can be made depending on whether the ratio of the dimension of the largest dynamical sector to that of its symmetry sector tends to zero or one in the thermodynamic limit, respectively (101, 102).”