Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations

Abstract

Stochastic processes with absorbing states feature remarkable examples of non-equilibrium universal phenomena. While a broad understanding has been progressively established in the classical regime, relatively little is known about the behavior of these non-equilibrium systems in the presence of quantum fluctuations. Here we theoretically address such a scenario in an open quantum spin model which in its classical limit undergoes a directed percolation phase transition. By mapping the problem to a non-equilibrium field theory, we show that the introduction of quantum fluctuations stemming from coherent, rather than statistical, spin-flips alters the nature of the transition such that it becomes first-order. In the intermediate regime, where classical and quantum dynamics compete on equal terms, we highlight the presence of a bicritical point with universal features different from the directed percolation class in low dimension. We finally propose how this physics could be explored within gases of interacting atoms excited to Rydberg states.

Keldysh field theory for driven open quantum systems

“…Here an example was provided recently in the context of driven Rydberg systems, where a short distance constraint in the coherent Hamilton dynamics gives rise to an additional relevant direction in parameter space, leading to a new kind of absorbing state phase transition without immediate counterpart in models of classical origin [327].…”

Numerical simulation of critical dissipative non-equilibrium quantum systems with an absorbing state

“…This means that, at criticality, different numerical methods or approaches to the dynamics can be compared by their ability to reproduce the expected power-laws. Furthermore, since the universality class of the QCP is currently debated, [7,9,11], it is of considerable interest in its own right to make estimates of critical exponents, comparing these with previous estimates and known cases.To simulate the non-equilibrium dynamics of the QCP, we apply matrix product states (MPSs) and the timeevolving block-decimation (TEBD) algorithm [13][14][15]. This algorithm belongs to a more general class of tensor network (TN) methods, well established for the simulation of closed quantum systems in 1d, which have also been applied to dissipative quantum systems previously in a number of cases [16][17][18][19][20][21][22][23][24].…”

“…This means that, at criticality, different numerical methods or approaches to the dynamics can be compared by their ability to reproduce the expected power-laws. Furthermore, since the universality class of the QCP is currently debated, [7,9,11], it is of considerable interest in its own right to make estimates of critical exponents, comparing these with previous estimates and known cases.…”

Epidemic Dynamics in Open Quantum Spin Systems

“…This permits the exploration of dynamical phenomena in settings which can be regarded as quantum generalizations of classical non-equilibrium systems [24,25]. A recent example is a quantum version of the so-called contact process [26,27], a simple stochastic model for population dynamics featuring a non-equilibrium phase transition [28] whose character changes drastically when moving from a purely-classical to a quantum regime.…”