Dynamical Quantum Phase Transition and Quasi Particle Excitation

Abstract

Dynamical phase transitions (DPTs) are signaled by the non-analytical time evolution of the dynamical free energy after quenching some global parameters in quantum systems. The dynamical free energy is calculated from the overlap between the initial and the time evolved states (Loschmidt amplitude). In a recent study it was suggested that DPTs are related to the equilibrium phase transitions (EPTs) (M. Heyl et al., Phys. Rev. Lett. \textbf{110}, 135704 (2013)). We here study an exactly solvable model, the extended $XY$ model, the Loschmidt amplitude of which provides a counterexample. We show analytically that the connection between the DPTs and the EPTs does not hold generally. Analysing also the general compass model as a second example, assists us to propound the physical condition under which the DPT occurs without crossing the equilibrium critical point, and also no DPT by crossing the equilibrium critical point.

10 pages, 5 figures; to appear in Scientific Reports

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Topological classification of dynamical phase transitions
• First order dynamical phase transitions
• Loschmidt Echo Revivals: Critical and Noncritical
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
• Universal quench dynamics of interacting quantum impurity systems
• Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
• Quantum phase transitions in exactly solvable one-dimensional compass models

Cited by in corpus (10)

• Dynamical Topological Quantum Phase Transitions at Criticality
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Dynamical quantum phase transition in a system of non-interacting bosons
• Ubiquity of zeros of Loschmidt amplitude for mixed states in different physical processes and their implications
• Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Exact zeros of the Loschmidt echo and quantum speed limit time for the dynamical quantum phase transition in finite-size systems
• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Entanglement in quenched extended Su-Schrieffer-Heeger model with anomalous dynamical quantum phase transitions