Efficient computation of lattice Green's functions for models with nearest-neighbour hopping

Department of Physics and Astronomy, University of British Columbia - Vancouver, BC, Canada V6T 1Z1

Received: 19 August 2010
Accepted: 28 October 2010

Abstract

We show that for models with nearest-neighbour (nn) hopping, the lattice Green's functions can be calculated without the need to perform integrals. Our method applies to rectangular, triangular and honeycomb lattices in two dimensions, and to simple, face-centered and body-centered lattices in three dimensions. External magnetic fields can be dealt with trivially. As an example, we show that our method works for any ratio φ/φ₀ of the magnetic flux through the unit cell, i.e. irrespective of the change in the size of the magnetic unit cell. Other straightforward generalizations are to models with multiple orbitals per site, with any spin-orbit coupling, on-site disorder, and any combinations thereof. The method works equally well in the presence of surfaces. In all cases, accurate values for large distances can be obtained very efficiently and without finite-size effects. The relationship to other computational methods is also analyzed.