On the Meaning of Berry Force For Unrestricted Systems Treated With Mean-Field Electronic Structure

TL;DR

This paper demonstrates that mean-field electronic structure methods can produce meaningful Berry forces in systems with spin unrestriction, especially in scattering scenarios, despite some interpretational and numerical challenges.

Contribution

It shows that approximate mean-field Berry forces can be physically meaningful in unrestricted systems and provides insights into their behavior near critical points.

Findings

Nonzero Berry force emerges with spin unrestriction

Mean-field Berry force approximates asymptotic scattering motion

Divergence occurs near Coulson-Fisher point

Abstract

We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction--even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fisher point (which can lead to numerical instabilities). We do not address magnetic fields here.