Isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian with only 1-electron interactions

TL;DR

This paper establishes an isomorphism between multi-state Hamiltonians and second-quantized many-electron Hamiltonians with only 1-electron interactions, enabling cross-application of methods and extending to models with 2-electron interactions.

Contribution

It introduces a formal isomorphism linking two Hamiltonian frameworks, allowing techniques for one to be applied to the other, including cases with 2-electron interactions.

Findings

Exact results for the Landauer model using classical mapping methods.

Methods applicable to second-quantized Hamiltonians with 2-electron interactions.

Demonstration of the isomorphism's utility in quantum transport models.

Abstract

We introduce the isomorphism between the multi-state Hamiltonian and the second-quantized many-electron Hamiltonian (with only 1-electron interactions). This suggests that all methods developed for the former can be employed for the latter, and vice versa. The resonant level (Landauer) model for nonequilibrium quantum transport is used as a proof-of-concept example. Such as the classical mapping models for the multi-state Hamiltonian proposed in our previous work [J. Chem. Phys. (submitted)] lead to exact results for this model problem. We further demonstrate how these methods can also be applied to the second-quantized many-electron Hamiltonian even when 2-electron interactions are included.