Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths

TL;DR

This paper introduces a comprehensive linear response theory for cavity QED materials applicable across all light-matter coupling regimes, including symmetry-broken phases, using two complementary approaches to analyze response functions.

Contribution

It develops and compares two novel methods for calculating response functions in cavity QED systems, validating mean-field decoupling and extending applicability to various models.

Findings

Both approaches produce identical response functions.

The theory applies to a broad class of cavity QED models.

It provides insights into finite-size effects and correlated systems.

Abstract

We develop a linear response theory for materials collectively coupled to a cavity that is valid in all regimes of light-matter coupling, including symmetry-broken phases. We present and compare two different approaches. First, using a coherent path integral formulation for the partition function to obtain thermal Green functions. This approach relies on a saddle point expansion for the action, that can be truncated in the thermodynamic limit. Second, by formulating the equations of motion for the retarded Green functions and solving them. We use a mean-field decoupling of high-order Green functions in order to obtain a closed, solvable system of equations. Both approaches yield identical results in the calculation of response functions for the cavity and material. These are obtained in terms of the bare cavity and material responses. In combination, the two techniques clarify the validity of a mean-field decoupling in correlated light-matter systems and provide complementary means to compute finite-size corrections to the thermodynamic limit. The theory is formulated for a general model that encompasses most of the systems typically considered in the field of cavity QED materials. Finally, we provide a detailed application of the theory to the Quantum Hall effect and to a collection of spin models.