Quantum Monte Carlo study of the cavity-coupled interacting electron gas

Using the auxiliary-field quantum Monte Carlo method, we study the interacting electron gas coupled to a cavity. While in the homogeneous case and the dipole approximation, the light-matter coupling in this model can still be solved analytically, we study the effect of a modulating external potential and - within an approximation - multiple photon modes carrying finite momentum. Our results inform ongoing efforts in developing improved functionals for the quantum electrodynamical density functional theory (QEDFT) and may shed light on the shortcomings of the dipole approximation in extended systems.