Gapless Excitation above a Domain Wall Ground State in a Flat Band Hubbard Model

TL;DR

This paper constructs exact ground states with domain walls in a flat-band Hubbard model, demonstrating gapless excitations above the domain wall state in higher dimensions and analyzing boundary condition effects.

Contribution

It introduces a class of exact ground states with domain walls and spiral structures in a deformed flat-band Hubbard model across arbitrary dimensions.

Findings

Existence of gapless excitations above domain wall ground states in dimensions > 1

Ground state degeneracy with all-spin-up or all-spin-down states under open boundary conditions

Energy gap in spin-wave excitations under periodic boundary conditions

Abstract

We construct a set of exact ground states with a localized ferromagnetic domain wall and with an extended spiral structure in a deformed flat-band Hubbard model in arbitrary dimensions. We show the uniqueness of the ground state for the half-filled lowest band in a fixed magnetization subspace. The ground states with these structures are degenerate with all-spin-up or all-spin-down states under the open boundary condition. We represent a spin one-point function in terms of local electron number density, and find the domain wall structure in our model. We show the existence of gapless excitations above a domain wall ground state in dimensions higher than one. On the other hand, under the periodic boundary condition, the ground state is the all-spin-up or all-spin-down state. We show that the spin-wave excitation above the all-spin-up or -down state has an energy gap because of the anisotropy.