Valence-bond states in dynamical Jahn-Teller molecular systems

TL;DR

This paper investigates valence-bond states in molecular systems with dynamical Jahn-Teller effects, revealing a ground state as a solid valence bond state in 1D and exploring doping effects.

Contribution

It introduces a novel exchange Hamiltonian for systems with local orbital degeneracy and dynamical Jahn-Teller effects, analyzing ground states and doping behavior.

Findings

Ground state in 1D is a valence bond solid.

In 2D, the ground state remains uncertain.

Doping effects in 1D are examined.

Abstract

We discuss a hopping model of electrons between idealized molecular sites with local orbital degeneracy and dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case (one electron per site and large Coulomb repulsions), in the simplest two-fold degenerate situation, we are led to consider a particular exchange hamiltonian, describing two isotropic spin-1/2 Heisenberg problems coupled by a quartic term on equivalent bonds. This twin-exchange hamiltonian applies to a physical regime in which the inter-orbital singlet is the lowest-energy intermediate state available for hopping. This regime is favored by a relatively strong electron-phonon coupling. Using variational arguments, a large-N limit, and exact diagonalization data, we find that the ground state, in the one dimensional case, is a solid valence bond state. The situation in the two dimensional case is less clear. Finally, the behavior of the system upon hole doping is studied in one dimension.