Scaling and Universality at Dynamical Quantum Phase Transitions

Area of Science:

• Quantum physics
• Condensed matter physics
• Statistical mechanics

Background:

• Dynamical quantum phase transitions (DQPTs) manifest as nonanalyticities in quantum systems undergoing real-time evolution out of equilibrium.
• A significant challenge lies in connecting DQPTs to fundamental concepts like scaling and universality, despite evidence of their link to equilibrium phase transitions.

Purpose of the Study:

• To establish a connection between DQPTs and equilibrium phase transitions by exploring scaling and universality.
• To demonstrate that DQPTs are critical points associated with unstable fixed points in equilibrium models.

Main Methods:

• Formulation of renormalization group transformations in complex parameter space for quantum quenches in Ising models.
• Numerical simulations to identify signatures of DQPTs in the dynamical buildup of spin correlations.

Main Results:

• DQPTs in Ising models are shown to be critical points linked to unstable equilibrium fixed points.
• These DQPTs exhibit universal scaling behavior, consistent with the universality class of the associated fixed point.
• Power-law scaling in spin correlations provides a measurable signature of DQPTs.

Conclusions:

• DQPTs are demonstrated to obey scaling and universality, bridging the gap between non-equilibrium dynamics and equilibrium phase transitions.
• The dynamical buildup of spin correlations offers an experimental pathway to observe and characterize this universal scaling.
• Future experiments with trapped ions could explore these dynamical scaling phenomena.