Discretization of Structured Bosonic Environments at Finite Temperature by Interpolative Decomposition: Theory and Application

TL;DR

This paper introduces a new low-rank decomposition method for discretizing bosonic spectral densities at finite temperature, improving simulation efficiency of open quantum systems and enabling applications to complex environments.

Contribution

The paper develops a novel interpolative decomposition technique for spectral density discretization, capturing temperature and frequency dependencies more effectively than existing methods.

Findings

Reduces degrees of freedom in quantum system simulations

Demonstrates improved accuracy over traditional discretization methods

Successfully applied to biological electron transfer models

Abstract

We present a comprehensive theory for a novel method to discretize the spectral density of a bosonic heat bath, as introduced in [H. Takahashi and R. Borrelli, J. Chem. Phys. \textbf{161}, 151101 (2024)]. The approach leverages a low-rank decomposition of the Fourier-transform relation connecting the bath correlation function to its spectral density. By capturing the time, frequency, and temperature dependencies encoded in the spectral density-autocorrelation function relation, our method significantly reduces the degrees of freedom required for simulating open quantum system dynamics. We benchmark our approach against existing methods and demonstrate its efficacy through applications to both simple models and a realistic electron transfer process in biological systems. Additionally, we show that this new approach can be effectively combined with the tensor-train formalism to investigate the quantum dynamics of systems interacting with complex non-Markovian environments. Finally, we provide a perspective on the selection and application of various spectral density discretization techniques.