Low energy electron-phonon effective action from symmetry analysis

TL;DR

This paper develops a symmetry-based method to derive low energy effective actions for electrons interacting with lattice vibrations, applicable to various lattice systems and orders.

Contribution

It introduces the concept of memory tensors for systematic derivation of effective actions, extending to arbitrary dimensions and derivative orders.

Findings

Re-derivation of Dirac fermions coupled to gauge fields on honeycomb lattice.

Derivation of low energy electron-phonon coupling in kagome lattice.

Method applicable to diverse lattice systems and symmetries.

Abstract

Based on a detailed symmetry analysis, we state the general rules to build up the effective low energy field theory describing a system of electrons weakly interacting with the lattice degrees of freedom. The basic elements in our construction are what we call the "memory tensors", that keep track of the microscopic discrete symmetries into the coarse-grained action. The present approach can be applied to lattice systems in arbitrary dimensions and in a systematic way to any desired order in derivatives. We apply the method to the honeycomb lattice and re-obtain the by now well-known effective action of Dirac fermions coupled to fictitious gauge fields. As a second example, we derive the effective action for electrons in the kagom\'e lattice, where our approach allows to obtain in a simple way the low energy electron-phonon coupling terms.