Nonadiabatic quantum geometry and optical conductivity

TL;DR

This paper introduces a dynamic quantum geometric tensor that links ground-state geometry to optical conductivity across frequencies, revealing the nongeometrical nature of the Drude response in metals.

Contribution

It presents a novel framework connecting ground-state quantum geometry with dynamic optical properties, extending geometric concepts to finite-frequency conductivity including metals and insulators.

Findings

The quantum metric-curvature tensor evolves causally in time.

The tensor encompasses the entire conductivity tensor at arbitrary frequencies.

The Drude term in metals is shown to be nongeometrical.

Abstract

The ground-state quantum geometry is at the root of several static and adiabatic properties, while genuinely dynamic properties are routinely addressed via Kubo formulae, whose essential entries are the excited states. It is shown here that the ground-state metric-curvature tensor evolves in time by means of a causal unitary operator, which by construction elucidates the geometrical effect of the excited states in compact form. In the condensed-matter case the generalized tensor encompasses the whole conductivity tensor at arbitrary frequencies in both insulators and metals, with the exception of the Drude term in the metallic case; the latter is shown to be eminently nongeometrical.