Abstract
Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient numerical simulation of large open systems in two spatial dimensions is a challenge. In this work, we develop a tensor network method, based on an infinite Projected Entangled Pair Operator (iPEPO) ansatz, applicable directly in the thermodynamic limit. We incorporate techniques of finding optimal truncations of enlarged network bonds by optimising an objective function appropriate for open systems. Comparisons with numerically exact calculations, both for the dynamics and the steady-state, demonstrate the power of the method. In particular, we consider dissipative transverse quantum Ising and driven-dissipative hard core boson models in non-mean field limits, proving able to capture substantial entanglement in the presence of dissipation. Our method enables to study regimes which are accessible to current experiments but lie well beyond the applicability of existing techniques.
Highlights
In recent experiments across a variety of architectures, the ability to sustain quantum correlations in a dissipative environment and study the evolution of strongly interacting many-body lattice systems in a precisely controlled manner has progressed enormously
Open quantum systems are often well described by a Lindblad master equation [21], which facilitates the study of a range of collective phenomena including nonequilibrium criticality [22,23,24,25,26,27], quantum chaos [28,29], and time crystallinity [30,31,32], many of which have no counterparts in closed systems at equilibrium
As a first benchmark of the algorithm, we simulate the dynamics of a dissipative transverse quantum Ising model with Hamiltonian σz j σzl hj;li þ
Summary
In recent experiments across a variety of architectures, the ability to sustain quantum correlations in a dissipative environment and study the evolution of strongly interacting many-body lattice systems in a precisely controlled manner has progressed enormously. In the context of dissipative or drivendissipative systems, we can reasonably expect that in many cases, dissipative processes should curtail the growth of entanglement and limit correlations generated by entangling dynamics; this is found to hold true in the fixed points of rapidly mixing dissipative quantum systems, which obey an area law [59,60,61] Despite this expectation, TN algorithms for open systems [62,63,64,65,66] have mostly been restricted to one-dimensional lattices, where the simple geometry plays a central role in the algorithm. SU is efficient, in order to integrate the equation of motion, it isolates a subsystem—for example, one unit cell—from the rest of the lattice and applies the dynamical map to the subsystem in isolation until a steady state is reached It has been questioned whether this approach can produce accurate results, and there are concerns over the convergence of this method in non-mean-field regimes [68].
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