Ergodicity breaking provably robust to arbitrary perturbations
- URL: http://arxiv.org/abs/2209.03966v2
- Date: Thu, 6 Oct 2022 02:50:32 GMT
- Title: Ergodicity breaking provably robust to arbitrary perturbations
- Authors: David T. Stephen, Oliver Hart and Rahul M. Nandkishore
- Abstract summary: We present a new route to ergodicity breaking via Hilbert space fragmentation that displays an unprecedented level of robustness.
In particular, our proof is not limited to symmetric perturbations, or to perturbations with long-range tails, or even to arbitrary geometrically nonlocal $k$-body perturbations.
- Score: 0.5735035463793008
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a new route to ergodicity breaking via Hilbert space fragmentation
that displays an unprecedented level of robustness. Our construction relies on
a single emergent (prethermal) conservation law. In the limit when the
conservation law is exact, we prove the emergence of Hilbert space
fragmentation with an exponential number of frozen configurations. We further
prove that every frozen configuration is absolutely stable to arbitrary
perturbations, to all finite orders in perturbation theory. In particular, our
proof is not limited to symmetric perturbations, or to perturbations with
compact support, but also applies to perturbations with long-range tails, and
even to arbitrary geometrically nonlocal $k$-body perturbations, as long as
$k/L \rightarrow 0$ in the thermodynamic limit, where $L$ is linear system
size. Additionally, we identify one-form $U(1)$ charges characterizing some
non-frozen sectors, and discuss the dynamics starting from typical initial
conditions, which we argue is best interpreted in terms of the
magnetohydrodynamics of the emergent one-form symmetry.
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