Ferromagnetic Domain Wall Ground States in One-Dimensional Deformed Flat-Band Hubbard Model

TL;DR

This paper constructs exact ferromagnetic domain wall ground states in a one-dimensional deformed flat-band Hubbard model, revealing spontaneous symmetry breaking and analyzing their properties and correlations.

Contribution

It introduces a new class of exact ground states with domain walls in a deformed flat-band Hubbard model, demonstrating their uniqueness, degeneracy, and physical properties.

Findings

Exact ground states with ferromagnetic domain walls constructed

Degeneracy with all-spin-up and all-spin-down states established

Cluster property and bounds of local observables proved

Abstract

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.