Onset of quantum thermalization in the Jahn-Teller model

We investigate the onset of quantum thermalization in a system governed by the Jahn-Teller Hamiltonian, which describes the interaction between a single spin and two bosonic modes. We find that the Jahn-Teller model exhibits a finite-size quantum phase transition between the normal phase and two types of super-radiant phase when the ratios of spin-level splitting to each of the two bosonic frequencies grow to infinity. We test the prediction of the eigenstate thermalization hypothesis in the Jahn-Teller model. We show that the expectation value of the spin observable quickly approaches its long-time average value. We find that the distance between the diagonal ensemble average and the microcanonical ensemble average of the spin observable decreases with the effective thermodynamic parameter. Furthermore, we show that the mean time fluctuations of the spin observable are small and are inversely proportional to the effective system dimension.