An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems

TL;DR

This paper introduces an exact method to compute the equilibrium reduced density matrix in excitonic systems, revealing how noise, disorder, and temperature influence localization and coherence, with applications to light-harvesting complexes.

Contribution

The paper presents a stochastic unraveling approach for the exact calculation of the equilibrium reduced density matrix, accounting for environmental effects in excitonic systems.

Findings

FMO is localized at low temperatures due to bias.

Disorder causes a plateau in coherence length in LH2.

Environmental noise can increase coherence length in biased systems.

Abstract

An exact method to compute the entire equilibrium reduced density matrix for systems characterized by a system-bath Hamiltonian is presented. The approach is based upon a stochastic unraveling of the influence functional that appears in the imaginary time path integral formalism of quantum statistical mechanics. This method is then applied to study the effects of thermal noise, static disorder, and temperature on the coherence length in excitonic systems. As representative examples of biased and unbiased systems, attention is focused on the well-characterized light harvesting complexes of FMO and LH2, respectively. Due to the bias, FMO is completely localized in the site basis at low temperatures, whereas LH2 is completely delocalized. In the latter, the presence of static disorder leads to a plateau in the coherence length at low temperature that becomes increasingly pronounced with increasing strength of the disorder. The introduction of noise, however, precludes this effect. In biased systems, it is shown that the environment may increase the coherence length, but only decrease that of unbiased systems. Finally it is emphasized that for typical values of the environmental parameters in light harvesting systems, the system and bath are entangled at equilibrium in the single excitation manifold. That is, the density matrix cannot be described as a product state as is often assumed, even at room temperature. The reduced density matrix of LH2 is shown to be in precise agreement with the steady state limit of previous exact quantum dynamics calculations.