Abstract
Lattice models of fermions, bosons, and spins have long served to elucidate the essential physics of quantum phase transitions in a variety of systems. Generalizing such models to incorporate driving and dissipation has opened new vistas to investigate nonequilibrium phenomena and dissipative phase transitions in interacting many-body systems. We present a framework for the treatment of such open quantum lattices based on a resummation scheme for the Lindblad perturbation series. Employing a convenient diagrammatic representation, we utilize this method to obtain relevant observables for the open Jaynes-Cummings lattice, a model of special interest for open-system quantum simulation. We demonstrate that the resummation framework allows us to reliably predict observables for both finite and infinite Jaynes-Cummings lattices with different lattice geometries. The resummation of the Lindblad perturbation series can thus serve as a valuable tool in validating open quantum simulators, such as circuit-QED lattices, currently being investigated experimentally.
Highlights
Lattice models describe particles or spins residing on a set of sites, arranged in a regular fashion
Lattice models can cover a large arena of physical systems and phenomena
Many studies of open quantum lattices have advanced our understanding of many-body systems under nonequilibrium conditions [14,17,24]
Summary
Lattice models describe particles or spins residing on a set of sites, arranged in a regular fashion. Typically include coherent driving and photon loss [51] Such systems will be a particular useful tool to better understand, gain intuition, and devise tractable effective models for open quantum lattices of interest. In the work presented here, we take a crucial step beyond finite-order perturbation theory by demonstrating a partial resummation of the perturbation series for the steady-state solution of the Lindblad master equation We employ this method to study an open Jaynes-Cummings (JC) lattice (Fig. 1) and establish that the resummation affords a significant improvement of the approximation accuracy.
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