Quantum phase transition and eigen microstate condensation in the quantum Rabi model

We introduce an eigen microstate approach (EMA) in the quantum system to describe the quantum phase transition without knowing the order parameter. Phases of a quantum system are determined by the so-called eigen microstates and their corresponding eigenvalues, which satisfy scaling relations in the critical regime. The quantum Rabi model (QRM) is taken as an example to demonstrate the validity of the EMA. Using both analytical and numerical calculations, we obtain the critical point, critical exponents, and scaling functions of the superradiant phase transition in the QRM. It suggests that a new phase emergency can be interpreted as a condensation of a specific eigen microstate. We expect that, in further studies, the EMA will be applied to more complex quantum phase transition problems in which order parameters cannot be easily defined.