Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices. (21st January 2019)

• Record Type: Journal Article
• Authors: Lesanovsky, Igor; Macieszczak, Katarzyna; Garrahan, Juan P
• Is Part Of: Quantum science and technology. Volume 4:Number 2(2019)
• Publication Date: 2019-01-21
• Subjects: phase transitions -- quantum simulation -- quantum maps -- Rydberg atoms -- cellular automata; Quantum theory -- Periodicals; Quantum theory; Periodicals; 530
• DOI: 10.1088/2058-9565/aaf831
• Languages: English
• ISSNs: 2058-9565

Abstract

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, and 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.