Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments

TL;DR

This paper compares methods for modeling temperature effects in strongly coupled open quantum systems with structured environments, demonstrating the effectiveness of T-TEDOPA and HEOM in different temperature regimes through specific examples.

Contribution

It introduces a comparative analysis of T-TEDOPA and HEOM approaches, highlighting their efficiency and applicability in simulating temperature-dependent quantum dynamics.

Findings

T-TEDOPA effectively simulates finite-temperature dynamics with continuous spectral densities.

HEOM efficiently models low-temperature regimes using complex poles of spectral densities.

Both methods successfully simulate complex quantum systems like phenylene ethynylene dimers.

Abstract

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials (T-TEDOPA) formalism in Hilbert space remains challenging. We compare different manners of modeling the environment. Sampling the Fourier transform of the bath correlation function, also called temperature dependent spectral density, proves to be very effective. T-TEDOPA (Tamascelli et al. Phys. Rev. Lett. 123, 090402 (2019)) uses a linear chain of oscillators with positive and negative frequencies while HEOM is based on the complex poles of an optimized rational decomposition of the temperature dependent spectral density (Xu et al. Phys. Rev. Lett. 129, 230601 (2022)). Resorting to the poles of the temperature independent spectral density and of the Bose function separately is an alternative when the problem due to the huge number of the Bose poles at low temperature is circumvented. Two examples illustrate the effectiveness of the HEOM and T-TEDOPA approaches: a benchmark pure dephasing case and a two-bath model simulating dynamics of excited electronic states coupled through a conical intersection. We show the efficiency of T-TEDOPA to simulate dynamics at a finite temperature by using either continuous spectral densities or only all the intramolecular oscillators of a linear vibronic model calibrated from ab initio data of a phenylene ethynylene dimer.