Dissecting Superradiant Phase Transition in the Quantum Rabi Model

Phase transitions are both thermodynamically and quantum-mechanically ubiquitous in nature and laboratories, and their understanding remains one of the most active issues in modern physics and related disciplines. The Landau theory provides a general framework to describe phenomenologically phase transitions by introducing order parameters and associated symmetry breaking. This theory is also taken as a starting point to explore critical phenomena in connection with phase transitions in the renormalization group, which provides a complete theoretical description of behaviors close to critical points. In this context, the microscopic mechanism of phase transitions remains unclear. In this study, we explore the microscopic mechanism of the superradiant phase transition in the quantum Rabi model (QRM). First, we perform a diagonalization operation in an operator space to obtain three fundamental patterns, denoted as λ₁, λ₂, and λ₃, involved in the QRM. Then, we explicitly analyze the energy evolutions of these patterns with increasing coupling strength. The observed characteristic behaviors reveal the microscopic mechanism of the superradiant phase transition as a consequence of competition between patterns due to different phase relations. In other words, with increasing coupling strength, the pattern λ₁ drives the phase transition, the pattern λ₂ exhibits a similar response speed but less energy compensation than the pattern λ₁, and the pattern λ₃ exhibits a slow response speed but plays a key role in the balance between it and the pattern λ₁, which stabilizes the new phase. This type of dissecting mechanism explains why and how the superradiant phase transition occurs in the QRM and paves the way for exploring the microscopic mechanism of phase transitions that occur frequently in nature.