Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems

TL;DR

This paper introduces a uniform process tensor approach using MPOs to efficiently compute multi-time correlation functions in non-Markovian quantum systems, enabling spectral analysis without explicit real-time evolution.

Contribution

The authors develop a time-translation invariant MPO representation of the process tensor, improving numerical scaling and providing direct access to Fourier-space correlation functions.

Findings

Significantly improved numerical scaling for multi-dimensional spectra calculations.

Spectral representation of non-Markovian dynamics enables direct Fourier-space correlation functions.

Successful calculation of linear and 2D electronic spectra demonstrating the method's effectiveness.

Abstract

The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators (MPO) can be used for numerically exact calculations of multi-time correlation functions in systems strongly coupled to a non-Markovian reservoir. We show here that the numerical scaling for computing multi-dimensional spectra can be significantly improved using a time-translation invariant MPO representation of the process tensor obtained from the uniform time-evolving matrix product operator (uniTEMPO) method. In particular, this approach provides a spectral representation of the non-Markovian dynamics that gives direct access to correlation functions in Fourier-space, avoiding explicit real-time evolution. We calculate linear and 2D electronic spectra for an example system and discuss the performance and numerical scaling of our simulations.