Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics

TL;DR

This paper introduces a discrete-time quantum model on a 2D lattice exhibiting a continuous phase transition in excited spin density, linking quantum and classical non-equilibrium phenomena, with implications for Rydberg quantum simulators.

Contribution

It presents a novel discrete-time quantum dynamics model that captures non-equilibrium phase transitions and connects quantum correlations with classical automaton behavior.

Findings

Stationary state displays a continuous phase transition in spin excitation density.

Quantum correlations become long-ranged near the transition, similar to classical correlations.

Quantum correlations can sometimes be inferred from classical measurements.

Abstract

We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map is constructed such that the reduced state at each time step is separable. We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-called Domany-Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density-density correlations become long-ranged, but interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which - in a rather natural way - permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.