Ergodicity-breaking from Hilbert space fragmentation

2019. 06. 03. 14:15
Building F, Entrance III, seminar room of Department of Theoretical Physics
Tibor Rakovszky (TU Munich)

Event of the Exotic Quantum Phases Seminar Series:


Title: Ergodicity-breaking from Hilbert space fragmentation in dipole-conserving Hamiltonians


Abstract: "We show that the conservation of charge and dipole moment - 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 spin z component) and its associated dipole moment. First, we consider a minimal model with only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value, thus showcasing non-ergodic behavior. This absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local  basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including longer-range terms and find that they lead 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. Nevertheless, as long as the Hamiltonian has finite range, there are exponentially many states that do not thermalize, some of which we construct explicitly. Based on: P Sala, TR, R Verresen, M Knap, F Pollmann:"