Scaling behavior in the asymmetric quantum Rabi model

Abstract： The scaling behavior and critical exponents are examined in the asymmetric quantum Rabi model, where the parity symmetry is violated. A phase transition occurs in this model, allowing for the determination of critical exponents. A general scaling function is formulated, encompassing two scaling variables. Additionally, a quantum hyper-scaling relation between critical exponents is established. The investigation reveals that the scaling form remains applicable, employing an alternative scaling variable, even when the coupling is below the critical point. This discovery offers valuable insights into the experimental investigation of the super-radiant phase transition, particularly in the cavity platform, which has been limited by the well-known no-go theorem.