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arXiv:1705.00617 · Physical Review A

Solvable Markovian dynamics of lattice quantum spin models

D. Mesterházy, F. Hebenstreit

Published Jul 28, 2017• 9 citations
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Abstract

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.

DOI
10.1103/physreva.96.010104

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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.Wederive 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.Weestablish 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 N→∞, the coupling to the thermal bath destroys any long-range order.
We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic systems coupled to wideband reservoirs. This is done by providing an explicit correspondence between master equations and nonequilibrium Green's function approaches. Our findings permit us to address non-Markovian regimes characterized by negative decoherence rates and to characterize the dynamics with respect to a recently proposed measurement of ``non-Markovianity.'' We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding electronic model and XY\mathit{XY}XY spin chains. The rich set of nonequilibrium steady-state phases encountered extends previous results to the non-Markovian regime.
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We study the real-time evolution of large open quantum spin systems in two spatial dimensions, whose dynamics is entirely driven by a dissipative coupling to the environment. We consider different dissipative processes and investigate the real-time evolution from an ordered phase of the Heisenberg or XY model towards a disordered phase at late times, disregarding unitary Hamiltonian dynamics. The corresponding Kossakowski-Lindblad equation is solved via an efficient cluster algorithm. We find that the symmetry of the dissipative process determines the time scales, which govern the approach towards a new equilibrium phase at late times. Most notably, we find a slow equilibration if the dissipative process conserves any of the magnetization Fourier modes. In these cases, the dynamics can be interpreted as a diffusion process of the conserved quantity.