Critical Behavior of the Quantum Contact Process in One Dimension

authored by: Federico Carollo, Edward Gillman, Hendrik Weimer, Igor Lesanovsky
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.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): University of Nottingham
University of Tübingen
Type: Article
Journal: Physical review letters
Volume: 123
ISSN: 0031-9007
Publication date: 06.09.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.48550/arXiv.1902.04515 (Access: Open)
https://doi.org/10.1103/PhysRevLett.123.100604 (Access: Closed)

BibTeX

@article{56fed9d2bb794b11828c406fadbcb278,
title = "Critical Behavior of the Quantum Contact Process in One Dimension",
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.",
author = "Federico Carollo and Edward Gillman and Hendrik Weimer and Igor Lesanovsky",
note = "Funding text We thank Maryam Roghani, Matteo Marcuzzi, Jonathan Keeling, and Mari-Carmen Banuls for fruitful discussions. We are grateful for access to the University of Nottingham's Augusta HPC service. 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 No.A335266 (ESCQUMA)], the Engineering and Physical Sciences Council [Grants No.AEP/M014266/1, No.AEP/N03404X/1, and No.AEP/R04340X/1], the Leverhulme Trust [Grant No.ARPG-2018-181], the Volkswagen Foundation and the DFG within EXC 2123 (QuantumFrontiers), SFB 1227 (DQ-mat), and SPP 1929 (GiRyd). I.L. gratefully acknowledges funding through the Royal Society Wolfson Research Merit Award",
year = "2019",
month = sep,
day = "6",
doi = "10.48550/arXiv.1902.04515",
language = "English",
volume = "123",
journal = "Physical review letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "10",
}