Quantum phase crossover and chaos in generalized Jahn-Teller lattice model

TL;DR

This paper explores the quantum phase crossover and chaos phenomena in a generalized Jahn-Teller lattice model, revealing how fluctuations and boson frequency differences influence spectral statistics and phase behavior.

Contribution

It demonstrates the interplay of quantum fluctuations and boson frequency differences in phase crossover and spectral chaos within a generalized Jahn-Teller lattice model.

Findings

Identification of a crossover between quasi-normal and radiation domains.

Non-universal level-spacing distributions influenced by boson frequency differences.

Maximal level repulsions and chaos in the radiation domain.

Abstract

The generalized multispin Jahn-Teller model on a finite lattice or formally equivalent Dicke model extended to two long-wavelength coherent bosons of different frequencies is shown to exhibit a crossover between the polaron-modified "quasi-normal" and the squeezed "radiation" domains. We investigate effects of two kinds of interfering fluctuations on the phase crossover and on statistical characteristics of boson complex spectra: (i) Fluctuations in the electron subsystem- finite-size quantum fluctuations- are responsible for the dephasing of the coherence in the radiation domain and for the moderate occupation of the excited states in the normal domain. In the quasiclassical limit, radiation phase implies existence of a coherent acoustic super-radiant phase. (ii) Level-spacing fluctuations in excited boson level subsystem with strong level repulsions. Related probability distributions are shown to be non-universally spread between the limiting universal Wigner-Dyson and Poisson distributions. We proved that the difference in boson frequencies is responsible for reaching the most stochastic limit of the Wigner-Dyson distribution. Instanton lattice as a sequence of tunneling events in the most chaotic radiation domain exhibits maximal number of level-avoidings (repulsions). The non-universality of the distributions is caused by boson correlations which compete the level repulsions.