  Charge and energy transfer in biological and synthetic organic materials are
strongly influenced by the coupling of electronic states to high-frequency
underdamped vibrations under dephasing noise. Non-perturbative simulations of
these systems require a substantial computational effort and current methods
can only be applied to large systems with severely coarse-grained environmental
structures. In this letter, we introduce a dissipation-assisted matrix product
factorization (DAMPF) method based on a memory-efficient matrix product
operator (MPO) representation of the vibronic state at finite temperature. In
this approach, the correlations between environmental vibrational modes can be
controlled by the MPO bond dimension, allowing for systematic interpolation
between approximate and numerically exact dynamics. Crucially, by subjecting
the vibrational modes to damping, we show that one can significantly reduce the
bond dimension required to achieve a desired accuracy, and also consider a
continuous, highly structured spectral density in a non-perturbative manner. We
demonstrate that our method can simulate large vibronic systems consisting of
10-50 sites coupled with 100-1000 underdamped modes in total and for a wide
range of parameter regimes. An analytical error bound is provided which allows
one to monitor the accuracy of the numerical results. This formalism will
facilitate the investigation of spatially extended systems with applications to
quantum biology, organic photovoltaics and quantum thermodynamics.
