Fidelity Susceptibility And Quantum Phase Transitions In The Quantum Rabi Model

The phase transition describes the process of phase transformation in the physical system,not just the thermodynamic phase transition in the macroscopic field.In the microscopic field,there is also a quantum phase transition with a special phenomenon near the critical point.Quantum phase transitions usually only occur in multibody systems at extreme temperatures,but quantum Rabi models have recently been discovered—a model that describes a two-level atom coupled to a single model light field.In the Rabi model,when the ratio of the frequency of a two-level atom to the frequency of a light field approaches infinity,the model will exhibit a quantum phase transition from the normal phase to the super-radiation phase.In this paper,we study the quantum phase transition of the quantum Rabi model from the fidelity susceptibility extending from fidelity.This method avoids the traditional mean field theory and the Landau phase transition theory,and does not need to study the quantum phase transition by calculating the cumbersome order quantity and symmetry.We find that if the ratio between the frequency of the two-level atom and the frequency of the cavity field is finite,the fidelity susceptibility and the generalized adiabatic susceptibility will exhibit scaling behavior at a finite scale near the critical point of the phase transition of the quantum Rabi model..By analyzing the fidelity susceptibility by the scaling behavior at finite scale,we find that the scale rates of the fidelity susceptibility and the fourth-order generalized adiabatic susceptibility in the Rabi model are 4/3 and 2,respectively.At the same time,the correlation length critical index and the dynamic critical index are 3/2 and 1/3 respectively in the quantum threshold of the Rabi model.Since the fidelity susceptibility and the generalized adiabatic susceptibility are part of the quantum noise spectrum,they can be directly measured by the linear response method.The scaling behavior of the fidelity susceptibility can be experimentally tested in the Rabi model.The simple structure of the quantum Rabi model is very useful for experimentally observing the scaling behavior of fidelity in quantum phase transitions.It also provides a simple and easy path for us to study quantum phase transitions.