A bosonic perspective on the classical mapping of fermionic quantum dynamics

TL;DR

This paper explores the classical mapping of fermionic quantum dynamics using the Meyer-Miller Hamiltonian, comparing it with other mappings, and finds that the MM mapping can accurately reproduce one-body density dynamics even in interacting systems.

Contribution

It demonstrates that the Meyer-Miller classical mapping is exact for non-interacting fermions and compares its performance with other fermionic mappings, revealing its effectiveness in complex models.

Findings

MM mapping is exact for non-interacting fermions.

Including fermionic anti-symmetry via Jordan-Wigner does not improve mapping accuracy.

MM and LMM mappings can capture interference effects in energy transfer models.

Abstract

We consider the application of the original Meyer-Miller (MM) Hamiltonian to mapping fermionic quantum dynamics to classical equations of motion. Non-interacting fermionic and bosonic systems share the same one-body density dynamics when evolving from the same initial many-body state. The MM classical mapping is exact for non-interacting bosons, and therefore it yields the exact time-dependent one-body density for non-interacting fermions as well. Starting from this observation, the MM mapping is compared to different mappings specific for fermionic systems, namely the spin mapping (SM) with and without including a Jordan-Wigner transformation, and the Li-Miller mapping (LMM). For non-interacting systems, the inclusion of fermionic anti-symmetry through the Jordan-Wigner transform does not lead to any improvement in the performance of the mappings and instead it worsens the classical description. For an interacting impurity model and for models of excitonic energy transfer, the MM and LMM mappings perform similarly, and in some cases the former outperforms the latter when compared to a full quantum description. The classical mappings are able to capture interference effects, both constructive and destructive, that originate from equivalent energy transfer pathways in the models.