Tensor network influence functionals for open quantum systems with general Gaussian bosonic baths

TL;DR

This paper extends tensor network influence functional methods to simulate open quantum systems with complex, non-commuting Gaussian bosonic baths, ensuring accurate long-time dynamics and demonstrating applications to driven two-level systems.

Contribution

It introduces a generalized Gaussian influence functional for non-commuting system-bath couplings, enabling efficient long-time simulations with tensor networks.

Findings

Successfully simulated driven two-level emitters in bosonic lattices.

Ensured convergence for long evolution times with Trotter error handling.

Extended TEMPO method to more general system-bath interactions.

Abstract

Dynamics of open quantum systems with structured reservoirs can often be simulated efficiently with tensor network influence functionals. The standard variants of the time-evolving matrix product operator (TEMPO) method are applicable when the systems is coupled to Gaussian bosonic baths via hermitian coupling operators that mutually commute. In this work we introduce a generalization to cases where the system is coupled to a single reservoir through multiple non-commuting operators, representing the most general form of linear system-bath coupling. We construct a Gaussian influence functional that properly handles Trotter errors arising from a finite evolution time step, thus ensuring convergence for long evolution times. Based on this result, the uniform TEMPO scheme can be employed to obtain a matrix product operator form of the influence functional, enabling efficient simulations of the real-time dynamics of the open system. As a demonstration, we simulate the time evolution of driven two-level emitters coupled to a bosonic lattice at different lattice sites.