Finite Temperature Dynamical Density Matrix Renormalization Group for Spectroscopy in Frequency Domain.

We present a novel methodology through casting the dynamical density matrix renormalization group (DDMRG) into the matrix product state (MPS) formulation to calculate the spectroscopy at finite temperature for molecular aggregates. The frequency domain algorithm can avoid the time evolution accumulation of error and is naturally suitable for parallelization, in addition to facile graphic processing unit (GPU) acceleration. The high accuracy is demonstrated by simulating the optical spectra of vibronic model systems ranging from an exactly solvable dimer model to a more complex real-world perylene bisimide (PBI) J-aggregate. The relationship between the 0-0 emission strength and the exciton thermal coherent length is discussed for linearly stacked aggregates. The computing performance largely boosted by GPU demonstrates that DDMRG emerges as a promising method to study dynamical properties for complex systems.