2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

TL;DR

This paper introduces a numerical method using the Faddeev-LeVerrier algorithm to efficiently compute boundary Green's functions in two-dimensional topological systems, facilitating analysis of edge states in various models.

Contribution

It presents a novel application of the Faddeev-LeVerrier algorithm for calculating boundary Green's functions, improving computational efficiency over traditional recursive methods.

Findings

Efficient boundary Green's function computation demonstrated.

Applied to Chern insulators and topological superconductors.

Comparison shows improved performance over standard methods.

Abstract

Since the breakthrough of twistronics a plethora of topological phenomena in two dimensions has appeared, specially relating topology and electronic correlations. These systems can be typically analyzed in terms of lattice models of increasing complexity using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. As an illustration we apply our formalism to analyze the edge features of Chern insulators, topological superconductors as the Kitaev square lattice and the Checkerboard lattice in the flat band topological regime. The efficiency of the method is demonstrated by comparison to standard recursive Green's function calculations.