Green's functions on finite lattices and their connection to the infinite lattice limit

Abstract

It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of a translation operator. Explicit examples are given for one-and two-dimensional lattices.

Luttinger-liquid physics in wire and dot geometries

“…Note that the summation cannot be done analytically, recently developed approaches, cf. [Coj06] and [Coj07], only hold for energies outside the band. In the limiting case N x = 1, i. e. k x = π/2, the one-dimensional Green function (D.3) is re-obtained.…”