Ground-state spin structure of strongly interacting disordered 1D Hubbard model

We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite- U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron-electron repulsion, U , which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka (1) states that in theUD1limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown (2) that for open boundary conditions (BCs) the GS for finite U is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U , the GS of all spin sectors are degenerate. The problem of the interplay between disorder and interactions in systems of electrons is challenging and has a long history (3). It is of interest to study the influence of disorder on the possibility of forming a ferromagnetic GS. In this work we study the spin structure of the GS of a disorderedUD1Hubbard model in one dimension. We find that for periodic BCs as well as for open BCs, for any realization of on-site disorder, the GS is degenerate, where all spin sectors have the same lowest energy, except for the fully polarized one which has a higher energy. As a by-product of our proof we find that the GS of an even (odd) number of spinless fermions, on a one-dimensional (1D) ring threaded by flux, is minimal when the dimensionless flux 8=80 equals (0). This might be of interest for the study of persistent currents in disordered interacting 1D rings (4). Lieb and Mattis (2) have considered the 1D clean Hubbard model for any U< 1given hard wall (or open) BCs. They found that the GS is always a singlet (for an even number of spins). When U D1the GS in all the different spin sectors become degenerate. Here we present an analysis of UD1with periodic BCs, in the presence of on-site disorder. As will become clear later, the different BCs change the character of the problem and the periodic BC case gives us an insight into the higher dimensional variants of the problem. Some of the