Geometry of Contact Terms in Linear Response: Applications to Elasticity

TL;DR

This paper investigates how the geometry of strain perturbations affects the calculation of elastic moduli via linear response, resolving apparent contradictions and providing insights for experimental measurements in anisotropic systems.

Contribution

It introduces a geometric framework that corrects the Kubo response predictions for elastic moduli, reconciling quantum and classical elasticity theories.

Findings

Correction factors from strain space geometry resolve the energy conservation contradiction.

Contact terms can be experimentally observed using generalized f-sum rules.

The framework applies to anisotropic systems like electrons in magnetic fields.

Abstract

Employing the Kubo linear response formalism to calculate the elasticity of anisotropic systems has been shown to yield odd elastic moduli. For Hamiltonian systems, this result seems to be contradictory as it would violate energy conservation. To resolve this discrepancy, we examine the predictions of quantum linear response in the context of our expectation from classical elasticity theory. Our framework reveals that the geometry of the space of strain perturbations introduces correction factors to the correspondence between the Kubo formula and the elastic moduli which resolves the contradiction. We use a two-dimensional gas of electrons in a magnetic field as a pedagogical example. We use generalized f-sum rules to demonstrate how contact terms may reveal themselves in experimental measurements. Finally, we discuss the implications of our results for interpreting more general linear response functions.