The role of polarization field terms in a model for a cavity quantum material

Abstract

Constructing models for cavity quantum materials requires a careful treatment of the light-matter coupling. In general, one must specify matrix elements constructed from the material wavefunctions, which are often unknown in a tight-binding framework. The Peierls substitution is frequently used to avoid introducing these additional parameters in the multi-center dipole (or Peierls) gauge, under the assumption that contributions from intraband and interband dipole moments can be neglected. We present the derivation of the Peierls gauge description, including these dipole moment terms, in the passive view of canonical transformations. We construct a toy model for a multi-band system with two sites, which we couple to a uniform field in the Coulomb, dipole, and Peierls gauges. We find that all polarization field terms are required to describe multi-band coupling in the Peierls gauge. The Peierls substitution can only be justified under restriction to a single band in one dimension, provided one also ignores self-polarization corrections arising from bands outside the retained subspace. However, these corrections are frequently non-negligible. More generally, the Coulomb, dipole, and Peierls gauges define distinct partitions of the composite system into the light and matter subsystems. We illustrate the implications of this subsystem relativity for observables such as the photon number and on the performance of orbital truncations in each gauge.