Quantum Critical Scaling under Periodic Driving

TL;DR

This paper demonstrates that universal scaling laws in a quantum Ising model persist under periodic driving, with key quantities maintaining their scaling behavior up to a system-size-dependent time, indicating robustness of universality out-of-equilibrium.

Contribution

It shows that critical scaling in a quantum Ising model survives under sinusoidal periodic driving, extending the concept of universality to non-equilibrium conditions.

Findings

Scaling persists up to a time proportional to system size

Low-energy modes remain resilient to energy absorption

Universal features are maintained out-of-equilibrium

Abstract

Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behaviour is explained by noticing that the low-energy modes, responsible for the scaling properties, are resilient to the absorption of energy. Our results suggest that relevant features of the universality do hold also when the system is brought out-of-equilibrium by a periodic driving.