Non-equilibrium criticality in quench dynamics of infinite-range spin models

TL;DR

This paper investigates the non-equilibrium critical behavior of infinite-range spin models, specifically the Lipkin-Meshkov-Glick model, after a sudden quench, revealing three distinct universality classes characterized by different effective temperatures.

Contribution

It identifies and characterizes three distinct non-equilibrium universality classes in quench dynamics of the LMG model, including their critical exponents and effective temperatures.

Findings

Three universality classes: thermal, quantum, and non-equilibrium.

Effective temperature scales as finite, zero, and infinite with system size.

Analytical and numerical methods confirm the universality classes.

Abstract

Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick (LMG) model describing the collective interaction of $N$ spins, and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the quench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely non-equilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as $N^{1/3}$), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the non-equilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.