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

Year: 2021

Authors: Halimeh J.C., Van Damme M., Guo L., Lang J., Hauke P.

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

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.


Volume: 104 (11)      Pages from: 115133-1  to: 115133-14

More Information: We acknowledge support by Provincia Autonoma di Trento, the ERC Starting Grant StrEnQTh (Project ID 804305), Q@TN-Quantum Science and Technology in Trento-and the Collaborative Research Centre ISOQUANT (Project ID 273811115), Research Foundation Flanders (Grants No. G0E1520N and No. G0E1820N), and ERC grants QUTE (No. 647905) and ERQUAF (No. 715861).
KeyWords: renormalization-group; gauge-invariance; order; propagation; simulation
DOI: 10.1103/PhysRevB.104.115133