Hubbard Model on Decorated Lattices

TL;DR

This paper introduces a family of decorated lattices where the Hubbard model can be quasi-exactly solved, revealing an ordered chiral ground state and an effective XY model for low-energy excitations.

Contribution

It provides a rigorous solution for the ground state of the Hubbard model on decorated lattices and characterizes the low-energy chiral state as an XY model.

Findings

Ground state is an ordered array of local currents.

Low energy theory is an $S=1/2$ XY model.

Hubbard model solutions are quasi-exact on these lattices.

Abstract

We introduce a family of lattices for which the Hubbard model and its natural extensions can be quasi-exactly solved, i.e. solved for the ground and low energy states. In particular, we show rigorously that the ground state of the Hubbard model with off-site Coulomb repulsions on a decorated Kagom\`{e} lattice is an ordered array of local currents. The low energy theory describing this chiral state is an $S=1/2$ XY model, where each spin degree of freedom represents the two possible chiralities of each local current.