Nonlinear effects in E$\otimes(b_1+b_2)$ Jahn-Teller model: Variational approach with excited phonon states and mode correlations

TL;DR

This study investigates nonlinear and quantum effects in the E⊗(b₁+b₂) Jahn-Teller model using variational and numerical methods, revealing the importance of excited phonon states and mode correlations in different regimes.

Contribution

It introduces a variational approach incorporating excited phonon states and mode correlations, providing new insights into the ground state properties of the Jahn-Teller model.

Findings

Excited phonon states significantly affect the ground state in the self-trapping regime.

Localized oscillator states emerge in the tunneling regime.

Two-mode correlations become important near the E⊗e limit.

Abstract

Interplay of nonlinear and quantum effects in the ground state of the E$\otimes (b_1+b_2)$ Jahn-Teller model was investigated by the {\it variational approach and exact numerical simulations}. They result in the recognition of (i) importance of the admixture of {\it the first excited state of the displaced harmonic oscillator} of the symmetric phonon mode in the ground state of the system in the selftrapping-dominated regime; (ii) existence of {\it the region of localized $b_1$-undisplaced oscillator states} in the tunneling-dominated regime. The effect (i) occurs owing to significant decrease of the ground state energy on account of the overlapping contribution of the symmetric phonon mode between the states of the same parity. This contribution considerably improves variational results especially in the selftrapping-dominated regime. Close to the E$\otimes$e limit, the nonlinear effects of {\it two-mode correlations} turn to be effective due to the rotational symmetry of this case. In the tunneling-dominated regime the phonon wave functions behave like the strongly localized harmonic oscillator ground state and the effect (i) looses its significance.