Abstract
We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose–Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N, we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit , the coupling to the thermal bath destroys any long-range order.
Highlights
With the advent of ultracold gases and trapped ions as tunable quantum simulators, experiments are in the position to investigate the real-time evolution of quantum manybody systems directly with engineered model Hamiltonians [1,2,3]
Quantum Monte Carlo (QMC) methods are not limited by macroscopic quantum correlations, their application to nonequilibrium dynamics is hindered by a severe complex phase problem
We have established that the novel finite-size scaling behavior of the dissipative gap is insensitive to the choice of lattice discretization as, e.g., provided by the lattice geometry or boundary conditions
Summary
With the advent of ultracold gases and trapped ions as tunable quantum simulators, experiments are in the position to investigate the real-time evolution of quantum manybody systems directly with engineered model Hamiltonians [1,2,3]. For most of these systems the real-time evolution leading to the final state is less well understood It is known, that the dissipative contributions to the dynamics might close the hierarchy. While multilocal operators Lx1x2···xn, with n > 2, are conceivable and have been studied theoretically, e.g., in the context of steady states with nontrivial topology [45,46,47,48], local and bilocal operators appear to be sufficient to describe the phenomenology of engineered dissipative quantum spin-1/2 systems for BEC generation [27, 49]. The outline of this paper is as follows: In Sec. II we derive the closure conditions for hierarchies of correlation functions of quantum spin systems in the s = 1/2 representation in the case of open Markovian dynamics governed by local and bilocal jump operators. We conclude with an outlook on applications and possible further developments of this work
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