Current Response in Extended Systems as a Geometric Phase: Application to Variational Wavefunctions

TL;DR

This paper explores the linear current response in variational systems, revealing it can be expressed via a geometric phase, with implications for calculating transport properties in complex quantum states.

Contribution

It introduces a geometric phase framework for current response in variational wavefunctions, linking it to wavefunction properties and providing new insights into transport calculations.

Findings

Current response can be expressed as a geometric phase.

The geometric phase contribution is independent of projectors.

The Drude weight depends on exact energy eigenvalues, complicating calculations.

Abstract

The linear response theory for current is investigated in a variational context. Expressions are derived for the Drude and superfluid weights for general variational wavefunctions. The expression for the Drude weight highlights the difficulty in its calculation since it depends on the exact energy eigenvalues which are usually not available in practice. While the Drude weight is not available in a simple form, the linear current response is shown to be expressible in terms of a geometric phase, or alternatively in terms of the expectation value of the total position shift operator. The contribution of the geometric phase to the current response is then analyzed for some commonly used projected variational wavefunctions (Baeriswyl, Gutzwiller, and combined). It is demonstrated that this contribution is independent of the projectors themselves and is determined by the wavefunctions onto which the projectors are applied.