Hierarchical Equations of Motion Solved with the Multiconfigurational Ehrenfest Ansatz

Abstract: Being a numerically exact method for the simulation of dynamics in open quantum systems, the hierarchical equations of motion (HEOM) still suffers from the curse of dimensionality. In this study, we propose a novel MCE-HEOM method, which introduces the multiconfigurational Ehrenfest (MCE) ansatz to the second quantization formalism of HEOM. Here, the MCE equations of motion are derived from the time-dependent variational principle in a composed Hilbert-Liouville space, and each MCE coherent-state basis can be regarded as having an infinite hierarchical tier, such that the truncation tier of auxiliary density operators in MCE-HEOM can also be considered to be infinite. As demonstrated in a series of representative spin-boson models, our MCE-HEOM significantly reduces the number of variational parameters and could efficiently handle the strong non-Markovian effect, which is difficult for conventional HEOM due to the requirement of a very deep truncation tier. Compared with MCE, MCE-HEOM reduces the number of effective bath modes and circumvents the initial samplings for finite temperature, eventually resulting in a huge reduction of computational cost.