Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices
Garrahan, Juan P
Quantum Science and Technology
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Lesanovsky, I., Macieszczak, K., & Garrahan, J. P. (2019). Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices. Quantum Science and Technology, 4 (2), 02LT02-02LT02. https://doi.org/10.1088/2058-9565/aaf831
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.
The research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/2007-2013)/ERC [grant agreement number 335266 (ESCQUMA)], and was supported by the Engineering and Physical Sciences Council [grant numbers EP/M014266/1 and EP/R04340X/1] as well as the Leverhulme Trust [grant number RPG-2018-181]. IL gratefully acknowledges funding through the Royal Society Wolfson Research Merit Award.
External DOI: https://doi.org/10.1088/2058-9565/aaf831
This record's URL: https://www.repository.cam.ac.uk/handle/1810/291144
Attribution 4.0 International
Licence URL: http://creativecommons.org/licenses/by/4.0/
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