The SU(2) instanton and the adiabatic evolution of two Kramers doublets

TL;DR

This paper explores the adiabatic evolution of two Kramers doublets, revealing that the associated SU(2) non-Abelian geometric potential is equivalent to an SU(2) instanton, with implications for Jahn-Teller systems.

Contribution

It establishes a connection between the adiabatic evolution of Kramers doublets and SU(2) instantons, providing a new geometric perspective in Jahn-Teller systems.

Findings

The Hamiltonian is equivalent to a known Jahn-Teller system.

The SU(2) non-Abelian vector potential is explicitly shown to be an SU(2) instanton.

Various forms of the potentials are discussed.

Abstract

The adiabatic evolution of two doubly-degenerate (Kramers) levels is considered. The general five-parameter Hamiltonian describing the system is obtained and shown to be equivalent to one used in the $\Gamma_8 \otimes(\tau_2\oplus\epsilon)$ Jahn-Teller system. It is shown explicitly that the resulting SU(2) non-Abelian geometric vector potential is that of the (SO(5) symmetric) SU(2) instanton. Various forms of the potentials are discussed.