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- W4313549429 abstract "We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space ``shatters'' into dynamically disconnected subsectors. We identify this shattering as originating from the interplay of a $text{U}(1)$ conservation law and a one-form ${mathbb{Z}}_{2}$ constraint. We show that the number of dynamically disconnected sectors is exponential in system volume, and includes a subspace exponential in system volume within which the dynamics is exactly localized, even in the absence of quenched disorder. Depending on the emergent sector in which we work, the shattering can be weak (such that typical initial conditions thermalize with respect to their emergent symmetry sector), or strong (such that typical initial conditions exhibit localized dynamics). We present analytical and numerical evidence that a first-order-like ``freezing transition'' between weak and strong shattering occurs as a function of the symmetry sector, in a nonstandard thermodynamic limit. We further numerically show that on the ``weak'' (melted) side of the transition domain wall dynamics follows ordinary diffusion." @default.
- W4313549429 created "2023-01-06" @default.
- W4313549429 creator A5010150198 @default.
- W4313549429 creator A5011856527 @default.
- W4313549429 date "2022-12-21" @default.
- W4313549429 modified "2023-10-06" @default.
- W4313549429 title "Hilbert space shattering and dynamical freezing in the quantum Ising model" @default.
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- W4313549429 doi "https://doi.org/10.1103/physrevb.106.214426" @default.
- W4313549429 hasPublicationYear "2022" @default.
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