Mechanism of dynamical phase transitions: The complex-time survival amplitude

Abstract

Dynamical phase transitions are defined through non-analyticities of the survival probability of an out-of-equilibrium time-evolving state at certain critical times. They ensue from zeros of the corresponding survival amplitude. By extending the time variable onto the complex domain, we formulate the complex-time survival amplitude. The complex zeros of this quantity near the time axis correspond, in the infinite-size limit, to non-analytical points where the survival probability abruptly vanishes. Our results are numerically exemplified in the fully-connected transverse-field Ising model, which displays a symmetry-broken phase delimited by an excited-state quantum phase transition. A detailed study of the behavior of the complex-time survival amplitude when the characteristics of the out-of-equilibrium protocol changes is presented. The influence of the excited-state quantum phase transition is also put into context.

12+ pages, 9 figures, added comments

References in corpus (23)

• The large deviation approach to statistical mechanics
• The physics of exceptional points
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• Excited state quantum phase transitions in many-body systems
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Excited-state quantum phase transitions
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Impact of Quantum Phase Transitions on Excited Level Dynamics
• Coulomb analogy for nonhermitian degeneracies near quantum phase transitions
• Excited-state quantum phase transition in the Rabi model
• Dynamical Quantum Phase Transitions in Systems with Continuous Symmetry Breaking
• Dynamical and excited-state quantum phase transitions in collective systems
• Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems
• Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
• Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential
• Exceptional points near first- and second-order quantum phase transitions
• Excited-State Quantum Phase Transitions in the Anharmonic Lipkin-Meshkov-Glick Model I: Static Aspects
• Chaos in a deformed Dicke model
• Heat capacity for systems with excited-state quantum phase transitions

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