Prerequisites for relevant spectral density and convergence of reduced density matrices at low temperatures

TL;DR

This paper investigates conditions under which the spectral density can be simplified to reduce computational costs in low-temperature quantum dissipative systems, focusing on convergence of reduced density matrices.

Contribution

It identifies a prerequisite for spectral density that allows significant reduction of Matsubara terms needed for convergence at low temperatures.

Findings

Relevant spectral density can reduce Matsubara terms

Convergence of reduced density matrices is achievable with simplified spectral density

Low-temperature simulations become more computationally feasible

Abstract

Hierarchical equations of motion approach with the Drude-Lorentz spectral density has been widely employed in investigating quantum dissipative phenomena. However, it is often computationally costly for low-temperature systems because a number of Matsubara frequencies are involved. In this note, we examine a prerequisite required for spectral density, and demonstrate that relevant spectral density may significantly reduce the number of Matsubara terms to obtain convergent results for low temperatures.