Ground State of Quantum Jahn-Teller Model: Selftrapping vs Correlated Phonon-assisted Tunneling

TL;DR

This study investigates the ground state of the quantum Jahn-Teller model, revealing two dominant regimes—selftrapping and phonon-assisted tunneling—and compares variational results with exact numerical solutions.

Contribution

It introduces a variational approach to analyze the quantum Jahn-Teller model in lattice and local cases, highlighting the impact of quantum fluctuations and correlations.

Findings

Two parameter regions govern the ground state: selftrapping and tunneling.

Quantum fluctuations and correlations are significantly larger than reflection effects.

Variational results align well with numerical solutions away from transition regions.

Abstract

Ground state of the quantum Jahn-Teller model with broken rotational symmetry was investigated by the variational approach in two cases: a lattice and a local ones. Both cases differ by the way of accounting for the nonlinearity hidden in the reflection-symmetric Hamiltonian. In spite of that the ground state energy in both cases shows the same features: there appear two regions of model parameters governing the ground state: the region of dominating selftrapping modified by the quantum effects and the region of dominating phonon-assisted tunneling (antiselftrapping). In the local case (i) the effect of quantum fluctuations and anharmonicity due to the two-mode correlations is up to two orders larger than contributions due to the reflection effects of two-center wave function; (ii) the variational results for the ground state energy were compared with exact numerical results. The coincidence is the better the more far away from the transition region at the E$\otimes$e symmetry where the variational approach fails.