Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions

Jad C. Halimeh, Maarten Van Damme, Lingzhen Guo, Johannes Lang, and Philipp Hauke
Phys. Rev. B 104, 115133 – Published 20 September 2021

Abstract

In recent years, dynamical phase transitions and out-of-equilibrium criticality have been at the forefront of ultracold gases and condensed matter research. Whereas universality and scaling are established topics in equilibrium quantum many-body physics, out-of-equilibrium extensions of such concepts still leave much to be desired. Using exact diagonalization and the time-dependent variational principle in uniform matrix product states, we calculate the time evolution of the local order parameter and Loschmidt return rate in transverse-field Ising chains with antiferromagnetic power law-decaying interactions, and map out the corresponding rich dynamical phase diagram. Anomalous cusps in the return rate, which are ubiquitous at small quenches within the ordered phase in the case of ferromagnetic long-range interactions, are absent within the accessible timescales of our simulations in the antiferromagnetic case, showing that long-range interactions are not a sufficient condition for their appearance. We attribute this to much weaker domain-wall binding in the antiferromagnetic case. For quenches across the quantum critical point, regular cusps appear in the return rate and connect to the local order parameter changing sign, indicating the concurrence of two major concepts of dynamical phase transitions. Our results consolidate conclusions of previous works that a necessary condition for the appearance of anomalous cusps in the return rate after quenches within the ordered phase is for topologically trivial local spin flips to be the energetically dominant excitations in the spectrum of the quench Hamiltonian. Our findings are readily accessible in modern trapped-ion setups and we outline the associated experimental considerations.

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  • Received 4 July 2021
  • Accepted 10 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.115133

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsAtomic, Molecular & Optical

Authors & Affiliations

Jad C. Halimeh1,*, Maarten Van Damme2, Lingzhen Guo3, Johannes Lang4,†, and Philipp Hauke1,‡

  • 1INO-CNR BEC Center and Department of Physics, University of Trento, Via Sommarive 14, I-38123 Trento, Italy
  • 2Department of Physics and Astronomy, University of Ghent, Krijgslaan 281, 9000 Gent, Belgium
  • 3Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany
  • 4Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

  • *jad.halimeh@physik.lmu.de
  • gu53jup@pks.mpg.de
  • philipp.hauke@unitn.it

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Issue

Vol. 104, Iss. 11 — 15 September 2021

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