Numerical simulation of quantum nonequilibrium phase transitions without finite-size effects

Gillman, Edward; Carollo, Federico; Lesanovsky, Igor

Abstract

Classical (1 + 1)D cellular automata, as for instance Domany-Kinzel cellular automata, are paradigmatic systems for the study of non-equilibrium phenomena. Such systems evolve in discrete time-steps, and are thus free of time-discretisation errors. Moreover, they display non-equilibrium phase transitions which can be studied by simulating the evolution of an initial seed. At any finite time, this has support only on a finite light-cone. Thus, essentially numerically exact simulations free of finite-size errors or boundary effects are possible, leading to high accuracy estimates of critical exponents. Here, we show how similar advantages can be gained in the quantum regime: The many-body critical dynamics occurring in (1 + 1)D quantum cellular automata with an absorbing state can be studied directly on an infinite lattice when starting from seed initial conditions. This can be achieved efficiently by simulating the dynamics of an associated one-dimensional, non-unitary quantum cellular automaton using tensor networks. We apply our method to a model introduced recently and find accurate values for universal exponents, suggesting that this approach can be a powerful tool for precisely studying non-equilibrium universal physics in quantum systems. Introduction.-One of the most intriguing aspects of non-equilibrium phase transitions (NEPTs) is the emergence of universal behaviour: systems with very different microscopic details can display the same scaling laws at a macroscopic scale, both for key stationary and dynam-ical quantities. As in equilibrium, an understanding of such critical features comes from their classification into universality classes [1-3]. Each class groups systems with the same emergent behaviour, as identified by the values of parameters known as critical exponents. However, in contrast to equilibrium settings, even the simplest critical non-equilibrium systems, e.g. those featuring absorbing state phase transitions in the directed percolation (DP) universality class, are not analytically solvable and their exponents cannot be determined exactly.

Citation

Gillman, E., Carollo, F., & Lesanovsky, I. (2021). Numerical simulation of quantum nonequilibrium phase transitions without finite-size effects. Physical Review A, 103(4), Article L040201. https://doi.org/10.1103/physreva.103.l040201

• Journal Article Type: Article
• Acceptance Date: Mar 23, 2021
• Online Publication Date: Apr 8, 2021
• Publication Date: 2021-04
• Deposit Date: Mar 25, 2021
• Publicly Available Date: Apr 8, 2021
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 103
• Issue: 4
• Article Number: L040201
• DOI: https://doi.org/10.1103/physreva.103.l040201
• Public URL: https://nottingham-repository.worktribe.com/output/5414907
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.L040201