Dynamical quantum phase transitions: scaling and universality

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.

4 pages, 3 figures, minor changes, version as published

References in corpus (7)

• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Topological classification of dynamical phase transitions
• First order dynamical phase transitions
• Large deviations and universality in quantum quenches
• Dynamical quantum phase transitions in the axial next-nearest-neighbour Ising chain
• Quench echo and work statistics in integrable quantum field theories
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