Existence of the Spin-Wave Gap in a Deformed Flat-Band Hubbard Model

TL;DR

This paper proves the existence of a finite spin-wave gap in a deformed flat-band Hubbard model, demonstrating similarities with the XXZ model and providing bounds on the one-magnon energy spectrum.

Contribution

It establishes the presence of a spin-wave gap in a specific Hubbard model and relates its dispersion to the XXZ model, offering bounds on magnon energies.

Findings

Ground state is fully polarized (all spins up or down)

Spin-wave dispersion matches that of the XXZ model in certain parameters

Finite energy gap for spin waves in the model

Abstract

We consider a deformed flat-band Hubbard model under a periodic boundary condition in arbitrary dimensions. We show that the ground state is only all-spin-up or -down state. We obtain upper and lower bounds of the one-magnon spin-wave energy with an arbitrary momentum. This dispersion relation is the same as that in the XXZ model in the certain parameter region. Therefore the spin wave has a finite energy gap. These results suggests the our model and the XXZ model.