TY - JOUR

T1 - Critical Behavior of the Quantum Contact Process in One Dimension

AU - Carollo, Federico

AU - Gillman, Edward

AU - Weimer, Hendrik

AU - Lesanovsky, Igor

N1 - 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

PY - 2019/9/6

Y1 - 2019/9/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85072671917&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1902.04515

DO - 10.48550/arXiv.1902.04515

M3 - Article

C2 - 31573316

AN - SCOPUS:85072671917

VL - 123

JO - Physical review letters

JF - Physical review letters

SN - 0031-9007

IS - 10

M1 - 100604

ER -