Dynamical phase transitions in the two-dimensional transverse-field Ising model

Hashizume, Tomohiro and McCulloch, Ian P. and Halimeh, Jad C. (2022) Dynamical phase transitions in the two-dimensional transverse-field Ising model. Physical Review Research, 4 (1). 013250. ISSN 2643-1564 (https://doi.org/10.1103/PhysRevResearch.4.013250)

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Abstract

We investigate two separate notions of dynamical phase transitions in the two-dimensional nearest-neighbor transverse-field Ising model on a square lattice using matrix product states and a hybrid infinite time-evolving block decimation algorithm, where the model is implemented on an infinitely long cylinder with a finite diameter along which periodic boundary conditions are employed. Starting in an ordered initial state, our numerical results suggest that quenches below the dynamical critical point give rise to a ferromagnetic long-time steady state with the Loschmidt return rate exhibiting anomalous cusps even when the order parameter never crosses zero. Within the accessible timescales of our numerics, quenches above the dynamical critical point suggest a paramagnetic long-time steady state with the return rate exhibiting regular cusps connected to zero crossings of the order parameter. Additionally, our simulations indicate that quenching slightly above the dynamical critical point leads to a coexistence region where both anomalous and regular cusps appear in the return rate. Quenches from the disordered phase further confirm our main conclusions. Our work supports the recent finding that anomalous cusps arise only when local spin excitations are the energetically dominant quasiparticles. Our results are accessible in modern Rydberg experiments.

  • Item type:Article
    ID code:80986
    Dates:
    Date
    Event
    31 March 2022
    Published
    1 March 2022
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:09 Jun 2022 11:20
    Last modified:16 Apr 2024 04:06
    URI:https://strathprints.strath.ac.uk/id/eprint/80986
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