Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

TL;DR

This paper introduces a real-space decimation method to analyze open quantum systems described by Lindblad equations, providing analytical insights into their dynamics and steady states, demonstrated through driven-dissipative bosonic chains.

Contribution

The paper presents a novel decimation technique for calculating Green's functions in open quantum systems, enabling analytical solutions for complex dissipative dynamics.

Findings

Efficient analytical expressions for system dynamics and steady states.

Application to various bosonic chain models, including topologically non-trivial systems.

Demonstration of directional amplification linked to topology.

Abstract

The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.