Dynamical quantum phase transitions: scaling and universality

TL;DR

This paper establishes that dynamical quantum phase transitions (DQPTs) exhibit scaling and universality by linking them to equilibrium critical points through renormalization group analysis, supported by numerical simulations and experimental prospects.

Contribution

It formulates renormalization group transformations in complex parameter space for DQPTs, revealing their connection to equilibrium universality classes and critical phenomena.

Findings

DQPTs are associated with unstable fixed points of equilibrium Ising models.

Signatures of DQPTs show power-law scaling in spin correlations.

Dynamical scaling can be explored experimentally in trapped ion systems.

Abstract

Dynamical quantum phase transitions (DQPTs) at critical times appear as non-analyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.