Delocalization effect of the Hubbard repulsion in exact terms and two dimensions

Abstract

The genuine physical reasons explaining the delocalization effect of the Hubbard repulsion U are analyzed. First, it is shown that always when this effect is observed, U acts on the background of a macroscopic degeneracy present in a multiband type of system. After this step, I demonstrate that acting in such conditions, by strongly diminishing the double occupancy, U spreads out the contributions in the ground state wave function, hence strongly increases the one-particle localization length, and consequently extends the oneparticle behavior producing conditions for a delocalization effect. To be valuable, the reported results are presented in exact terms, being based on the first exact ground states deduced at half-filling in two dimensions for a prototype two band system, which is the generic periodic Anderson model at finite value of the interaction.

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“…For this reason we use the method based on positive semidefinite operator properties whose applicability does not depend on dimensionality and integrability [13][14][15][16] . The method has been previously applied in conditions unimaginable before in the context of exact solutions in 1-3D, even in the presence of the disorder [17][18][19][20][21][22][23][24] .…”

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“…There is also no delocalization error for multiple electron systems such as H. The delocalization effect of the Hubbard term has received attention in solid‐state physics31–34, but the origin of the effect is not as straightforward to analyze as in SCC‐DFTB.…”

Exact ground states for polyphenylene type of hexagon chains

“…To deduce exact ground states in such a case one uses a technique based on positive semidefinite operator properties whose applicability does not depend on dimensionality or integrability. The procedure itself has been described previously in details in several publications [16,17], provides results even in circumstances unexpected in the context of exact solutions as systems in two [18], or three [16] dimensions, disordered systems [19] or textures [20], being also intensively tested for chain structures [17,21,22] including hexagonal type of chains as well [23,24]. Using the method, one transforms the HamiltonianĤ in positive semidefinite form (i.e.Ĥ = nP n + E g , whereP n are positive semidefinite operators, while E g is a scalar) and looks for the most general wave vector |Ψ g with the property nP n |Ψ g = 0.…”

“…One notes that in (17) the parameters α, β, γ, δ are arbitrary, with the condition to satisfy the requirements W 1 = (γ|α| 2 /|β| 2 − α * )/(γ − 1) > 0, W 2 = (α * + δ|β| 2 )/(δ − 1) > 0, where W 1 , W 2 are real (see also the observation below (18)). The K 2 parameter is given by the relation¯…”