Onset of Quantum Thermalization in Jahn-Teller model

TL;DR

This paper studies how quantum thermalization occurs in the Jahn-Teller model, revealing a finite-size quantum phase transition and confirming the Eigenstate Thermalization Hypothesis through spin observable analysis.

Contribution

It demonstrates the presence of a quantum phase transition in the Jahn-Teller model and tests the Eigenstate Thermalization Hypothesis within this system.

Findings

Identification of a finite-size quantum phase transition.

Rapid approach of spin expectation to long-time average.

Small fluctuations inversely related to system size.

Abstract

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.