Interplay of entanglement and interactions in cavity light-matter systems

Cavity light-matter systems facilitate strong correlations between the photon field and fermions. Strong light-matter interactions have been shown to induce topological phase transitions in the electronic states and generate entanglement between fermions and photons. An outstanding challenge in calculating such entangled states is to obtain the many-body ground state within a controlled approximation method. Previous works have focused on calculating the ground state either numerically using DMRG methods, or using mean-field theory that is based on unentangled states, thus neglecting potential light-matter correlations. We propose an "entangled mean-field theory" in which we start with an entangled trial wavefunction as our ansatz and minimize the energy with respect to the parameters involved. This is expected to improve the accuracy of obtaining entangled electronic ground states in such systems. Along the way, we also resolve an issue arising from degeneracies in the single-particle spectrum that can lead to incorrect identification of entangled single-particle states.