Simulating vibronic spectra via Matsubara dynamics: coping with the sign problem

TL;DR

This paper develops a generalized Matsubara dynamics approach for simulating vibronic spectra across multiple potential energy surfaces, introducing a modified method that avoids the sign problem and accurately captures harmonic and anharmonic spectra.

Contribution

It extends Matsubara dynamics to multiple PESs using a local harmonic approximation and proposes a modified sampling method that bypasses the sign problem.

Findings

The modified method accurately reproduces vibronic spectra for harmonic systems.

The approach effectively handles anharmonic systems.

It avoids the sign problem in classical-like simulations.

Abstract

Measuring the vibronic spectrum probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this manuscript, we express the imaginary-time shifted time correlation function (TCF) and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. In contrast to the existing literature, we invoke a local harmonic approximation to the potential allowing an analytical evaluation of integrals. By subsequently applying the Matsubara approximation, we derive a generalization of the existing Matsubara method to multiple potential energy surfaces (PESs), which, however, suffers from the sign problem as its single-PES counterpart does. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to simulate the standard correlation function via classical-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and it yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system, but also for an anharmonic one.