Critical Behavior of the Quantum Contact Process in One Dimension

Federico Carollo, Edward Gillman, Hendrik Weimer, and Igor Lesanovsky
Phys. Rev. Lett. 123, 100604 – Published 6 September 2019
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Abstract

The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple—especially in one dimension—results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.

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  • Received 25 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.100604

© 2019 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Federico Carollo1,2, Edward Gillman1,2, Hendrik Weimer3, and Igor Lesanovsky1,2,4

  • 1School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 2Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 3Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
  • 4Institut für Theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

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Issue

Vol. 123, Iss. 10 — 6 September 2019

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