One-Shot Simulation of Static Disorder in Quantum Dynamics with Equilibrium Initial State via Matrix Product State Sampling

TL;DR

This paper introduces an extended matrix product state method that efficiently simulates static disorder effects in quantum dynamics, significantly reducing computational costs and enabling large-scale sampling in complex molecular systems.

Contribution

The authors develop a one-shot MPS sampling technique for static disorder in quantum systems, improving efficiency over traditional methods and handling correlated initial states.

Findings

Accurately captures static disorder effects with moderate MPS bond dimension increase.

Reduces computational cost compared to direct sampling methods.

Enables generation of many samples with negligible additional cost.

Abstract

Static disorder plays a crucial role in the electronic dynamics and spectroscopy of complex molecular systems. Traditionally, obtaining observables averaged over static disorder requires thousands of realizations via direct sampling of the disorder distribution, leading to high computational costs. In this work, we extend the auxiliary degree-of-freedom based matrix product state (MPS) method to handle system-bath correlated thermal equilibrium initial states. We validate the effectiveness of the extended method by computing the dipole-dipole time correlation function of the Holstein model relevant to the emission spectrum of molecular aggregates. Our results show that the method accurately captures static disorder effects using a one-shot quantum dynamical simulation, with only a moderate increase in MPS bond dimension, thereby significantly reducing computational cost. Moreover, it enables the generation of a much larger number of samples than the conventional direct sampling method at negligible additional cost, thus reducing statistical errors. This method provides a broadly useful tool for calculating equilibrium time correlation functions in system-bath coupled models with static disorder.