Lattice Green's functions for kagome, diced and hyperkagome lattices

TL;DR

This paper derives lattice Green's functions and density of states for kagome, diced, and hyperkagome lattices, providing new analytical insights and numerical validations for these complex 3D lattice models.

Contribution

It rederives key properties for kagome and diced lattices and suggests a potential closed-form solution for the hyperkagome lattice's density of states.

Findings

DOS and LGF at the origin for kagome and diced lattices are rederived

Numerical checks confirm the derived formulas

Hyperkagome lattice shows a continuous energy spectrum and a zero in the DOS

Abstract

Lattice Green's functions (LGF) and density of states (DOS) for non-interacting models on 3 related lattices are presented. The DOS and LGF at the origin for the kagome and diced lattices are rederived. Furthermore, from the form obtained for the DOS of the hyperkagome lattice, it seems highly suggestive that a closed form expression can be obtained if a particular complicated yet highly symmetrical integral can be solved. The results have been checked numerically. The continuum of energy states in the hyperkagome lattice and the appearance of a zero in the kagome lattice may be explicitly seen from the formulae obtained.