Localization and spectrum of quasiparticles in a disordered fermionic Dicke model

We study a fermionic two-band model with the interband transition resonantly coupled to a cavity. This model was recently proposed to explain cavity-enhanced charge transport, but a thorough characterization of the closed system, in particular localization of various excitations, is lacking. In this work, using exact diagonalization, we characterize the system by its spectrum under various filling factors and variable disorder. As in the Dicke model, the effective light-matter coupling scales with the square root of the system size. However, there is an additional factor that decreases with increasing doping density. The transition from the weak-coupling regime to the strong-coupling regime occurs when the effective light-matter coupling is larger than the electronic bandwidth. Here, the formation of exciton-polaritons is accompanied by the formation of bound excitons. Photon spectral functions exhibit significant weights on the in-gap states between the polaritons, even without disorder. Finally, while the localization of electron-hole excitations in a disordered system is lifted by strong coupling, the same is not true for free charges, which remain localized at strong and even ultrastrong coupling. Based on this finding, we discuss scenarios for charge transport

Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system

We study dynamical quantum phase transitions (DQPTs) in the extended Bose-Hubbard model after a sudden quench of the nearest-neighbor interaction strength. Using the time-dependent density matrix renormalization group, we demonstrate that interaction-driven DQPTs can appear after quenches between two topologically trivial insulating phases -- a phenomenon that has so far only been studied between gapped and gapless phases. These DQPTs occur when the interaction strength crosses a certain threshold value that does not coincide with the equilibrium phase boundaries, which is in contrast to quenches that involve a change of topology. In order to elucidate the nonequilibrium excitations during the time evolution, we define a new set of string and parity order parameters. We find a close connection between DQPTs and these newly defined order parameters for both types of quenches. In the interaction-driven case, the order parameter exhibits a singularity at the time of the DQPT only when the quench parameter is close to the threshold value. Finally, the timescales of DQPTs are scrutinized and different kinds of power laws are revealed for the topological and interaction-driven cases.Comment: 6 pages, 4 figures, and supplemental materia