Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices

TL;DR

This paper introduces a resummation framework for Lindblad perturbation series to analyze open quantum lattice models, enabling accurate predictions of observables in complex systems like the Jaynes-Cummings lattice, aiding quantum simulation validation.

Contribution

It develops a novel resummation scheme for Lindblad perturbation series using a diagrammatic approach, specifically applied to open quantum lattices such as the Jaynes-Cummings model.

Findings

Reliable prediction of observables for finite and infinite lattices.

Effective validation tool for open quantum simulators.

Applicable to various lattice geometries.

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.