Origami rules for the construction of localized eigenstates of the Hubbard model in decorated lattices

TL;DR

This paper introduces a systematic method to construct exact localized many-body eigenstates of the Hubbard model in decorated lattices, applicable for both non-interacting and strongly interacting regimes, by exploiting lattice symmetries and folding rules.

Contribution

It provides a novel set of rules for constructing localized eigenstates in decorated lattices, extending the understanding of localization in the Hubbard model across interaction regimes.

Findings

Localized eigenstates can be constructed using symmetry-based folding rules.

The method applies to both U=0 and U→∞ regimes of the Hubbard model.

The approach enables systematic design of localized states in complex lattice geometries.

Abstract

We present a method of construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for $U=0$ and $U\rightarrow\infty$. These states are localized in what concerns both hole and particle movement. The starting point of the method is the construction of a plaquette or a set of plaquettes with a higher symmetry than that of the whole lattice. Using a simple set of rules, the tight-binding localized state in such a plaquette can be divided, folded and unfolded to new plaquette geometries. This set of rules is also valid for the construction of a localized state for one hole in the $U\rightarrow\infty$ limit of the same plaquette, assuming a spin configuration which is a uniform linear combination of all possible permutations of the set of spins in the plaquette.