Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State

Gillman, Edward; Carollo, Federico; Lesanovsky, Igor

Abstract

The simulation of out-of-equilibrium dissipative quantum many body systems is a problem of fundamental interest to a number of fields in physics, ranging from condensed matter to cosmology. For unitary systems, tensor network methods have proved successful and extending these to open systems is a natural avenue for study. In particular, an important question concerns the possibility of approximating the critical dynamics of non-equilibrium systems with tensor networks. Here, we investigate this by performing numerical simulations of a paradigmatic quantum non-equilibrium system with an absorbing state: the quantum contact process. We consider the application of matrix product states and the time-evolving block decimation algorithm to simulate the time-evolution of the quantum contact process at criticality. In the Lindblad formalism, we find that the Heisenberg picture can be used to improve the accuracy of simulations over the Schrodinger approach, which can be understood by considering the evolution of operator-space entanglement. Furthermore, we also consider a quantum trajectories approach, which we find can reproduce the expected universal behaviour of key observables for a significantly longer time than direct simulation of the average state. These improved results provide further evidence that the universality class of the quantum contact process is not directed percolation, which is the class of the classical contact process.

Citation

Gillman, E., Carollo, F., & Lesanovsky, I. (2019). Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State. New Journal of Physics, 21, Article 093064. https://doi.org/10.1088/1367-2630/ab43b0

• Journal Article Type: Article
• Acceptance Date: Sep 2, 2019
• Online Publication Date: Sep 30, 2019
• Publication Date: Sep 30, 2019
• Deposit Date: Sep 19, 2019
• Publicly Available Date: Sep 30, 2019
• Journal: New Journal of Physics
• Electronic ISSN: 1367-2630
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Article Number: 093064
• DOI: https://doi.org/10.1088/1367-2630/ab43b0
• Keywords: General Physics and Astronomy
• Public URL: https://nottingham-repository.worktribe.com/output/2634932
• Publisher URL: https://iopscience.iop.org/article/10.1088/1367-2630/ab43b0
• Additional Information: Journal title: New Journal of Physics; Article type: paper; Article title: Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state; Copyright information: © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft; License information: cc-by Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.; Date received: 2019-07-11; Date accepted: 2019-09-11; Online publication date: 2019-09-30
• Contract Date: Sep 19, 2019