  We construct a set of exact ground states with a localized ferromagnetic
domain wall and an extended spiral structure in a quasi-one-dimensional
deformed flat-band Hubbard model. In the case of quarter filling, we show the
uniqueness of the ground state with a fixed magnetization. The ground states
with these structures are degenerate with the all-spin-up and all-spin-down
states. This property of the degeneracy is the same as the domain wall
solutions in the XXZ Heisenberg-Ising model. We derive a useful recursion
relation for the normalization of the domain wall ground state. Using this
recursion relation, we discuss the convergence of the ground state expectation
values of arbitrary local operators in the infinite-volume limit. In the ground
state of the infinite-volume system, the translational symmetry is
spontaneously broken by this structure. We prove that the cluster property
holds for the domain wall ground state and excited states. We also estimate
bounds of the ground state expectation values of several observables, such as
one- and two-point functions of spin and electron number density.
