Graduate Green's function calculation of an infinite lattice with periodicity in 1D

[paulhj]

TL;DR

How do I numerically compute the Green's function matrix for an infinitely long lattice with some complicated unit cell?

I am currently trying to compute the Green's function matrix of an infinite lattice with a periodicity in 1 dimension in the tight binding model. I have matrix $V$ that describes the hopping of electrons within each unit cell, and a matrix $W$ that describes the hopping between unit cells.
By Fourier transforming and diagonalising the resulting matrix I have been able to calculate the energy band structure of the system as a function of momentum in the direction of periodicity. Is there then a way of numerically calculating the Green's function matrix of this system, similar to how you can calculate the Green's function for an infinite chain? Any help or recommended reading is much appreciated.

 

[peterwang]

For a finite system, computing Green's function is easy: to compute (zI-H)^-1. If you are only interested in a subsystem of a finite system, the concept of self-energy can be introduced. The self-energy is more helpful when you considering an infinite system. I suppose you want the Green's function of a subsystem inside the infinite lattice, then the problem is an embedding problem: the environment around the subsystem provide self-energy to the subsystem in question, the self-energy can be computed from the surface green function of the semi-infinite system.