Scaling and Universality at Ramped Quench Dynamical Quantum Phase Transition

Abstract

The nonequilibrium dynamics of a periodically driven extended XY model, in the presence of linear time dependent magnetic filed, is investigated using the notion of dynamical quantum phase transitions (DQPTs). Along the similar lines to the equilibrium phase transition, the main purpose of this work is to search the fundamental concepts such as scaling and universality at the ramped quench DQPTs. We have shown that the critical points of the model, where the gap closing occurs, can be moved by tuning the driven frequency and consequently the presence/absence of DQPTs can be flexibly controlled by adjusting the driven frequency. %Taking advantage of this property, We have uncovered that, for a ramp across the single quantum critical point, the critical mode at which DQPTs occur is classified into three regions: the Kibble-Zurek (KZ) region, where the critical mode scales linearly with the square root of the sweep velocity, pre-saturated (PS) region, and the saturated (S) region where the critical mode makes a plateau versus the sweep velocity. While for a ramp that crosses two critical points, the critical modes disclose just KZ and PS regions. On the basis of numerical simulations, we find that the dynamical free energy scales linerly with time, as approaches to DQPT time, with the exponent $\nu =1\pm 0.01$ for all sweep velocities and driven frequencies.

11 pages

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Topological classification of dynamical phase transitions
• Mixed state dynamical quantum phase transition and emergent topology
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Loschmidt Echo Revivals: Critical and Noncritical
• Dynamical Quantum Phase Transition and Quasi Particle Excitation
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dynamical quantum phase transitions in the quantum Potts chain
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility
• Dynamical quantum phase transition from a critical quantum quench
• Dynamical quantum phase transition in a system of non-interacting bosons
• Topological dynamical quantum phase transition in a quantum skyrmion phase
• Dynamical quantum phase transitions in a mesoscopic superconducting system
• Quench dynamics and scaling laws in topological nodal loop semimetals
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Dissipation driven dynamical topological phase transitions in two-dimensional superconductors
• Lindblad master equation approach to the dissipative quench dynamics of planar superconductors
• Complex dynamics approach to dynamical quantum phase transitions: the Potts model

Cited by in corpus (8)

• Competition of long-range interactions and noise at ramped quench dynamical quantum phase transition: The case of the long-range pairing Kitaev chain
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions
• Dynamics of decoherence in a noisy driven environment
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models
• Topological Classification of Dynamical Quantum Phase Transitions in the 1D XY model via Critical Mode Analysis
• Universal features of non-analytical energy storage in quantum critical quantum batteries