Nagaoka State and Degeneracy in the U=infinity Hubbard Model

TL;DR

This paper investigates the U=infinity Hubbard model on a hypercubic lattice with one or more holes, revealing degeneracies in the maximal-spin sector and constructing states with lower energy than the Nagaoka state.

Contribution

It provides a variational proof that the Nagaoka state is not always the ground state when degeneracy occurs and explicitly constructs lower-energy incommensurate spin-wave states.

Findings

Degeneracy can occur in the maximal-spin sector.

The Nagaoka state is not always the ground state when degeneracy exists.

Explicit construction of lower-energy spin-wave states.

Abstract

The U=infinity Hubbard model on a hypercubic lattice with exactly one hole is studied. It is seen that a degeneracy can occur in the maximal-spin sector. It is proved variationally that the Nagaoka (maximal spin) state is not a ground state, if degeneracy exists. We give an explicit construction of a variational state, an incommensurate spin-wave state, with energy lower than that of the Nagaoka state. For the case of more than one hole, a few examples are discussed where a degeneracy exists.