Diversity of Superradiant Phase Transitions in the Bose-Fermi System under Tight-Binding Model in the Weak-Coupling Regime

We present a comprehensive analysis of the dynamic diversity associated with superradiant phase transitions within a one-dimensional tight-binding electronic chain that is intrinsically coupled to a single-mode optical cavity. By employing the quantized electromagnetic vector potential through the Peierls substitution, the gauge-invariant coupled Bose-Fermi system facilitates momentum-dependent superradiant transitions and effectively avoids the second-order spurious phase transitions typically observed in Dicke-like models. The quantum phase transitions in this system are characterized by stable dynamics, including the displacement and squeezing of the cavity mode and the redistribution of electronic momentum in the solid chain. Distinct from multimode cavity QED systems with atomic gases, this single-mode optical configuration unveils a range of nonlinear phenomena, including multistability and diversity of spontaneous symmetry breaking. The setup allows for precise manipulation of superradiant phases in the weak coupling regime, effectively mitigating the adverse effects of quantum fluctuation divergences. The diverse attributes of these quantum phase transitions enhance our understanding of tunable quantum solid devices and underscore their potential applications in quantum information processing and metrology.