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

by Miguel Alvarado and Alfredo Levy Yeyati

This Submission thread is now published as SciPost Phys. 13, 009 (2022)

Submission summary

As Contributors: Miguel Alvarado
Preprint link: scipost_202109_00011v3
Code repository: https://zenodo.org/record/6126504
Date accepted: 2022-06-21
Date submitted: 2022-03-09 17:53
Submitted by: Alvarado, Miguel
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational

Abstract

Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models 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. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lattice hosting topological flat bands. The efficiency and accuracy of the method is demonstrated by comparison to standard recursive Green's function calculations and direct diagonalizations.

Published as SciPost Phys. 13, 009 (2022)



List of changes

Dear editor,
Thank you for the referee reports on our manuscript.
1. We have modified the introduction of the manuscript in accordance with their comments to clarify the main objective of the paper, the conceptual basis of it and the purpose of the method compared to other approaches.


Reports on this Submission

Anonymous Report 1 on 2022-6-3 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202109_00011v3, delivered 2022-06-03, doi: 10.21468/SciPost.Report.5176

Report

This article is part of a series of works by the authors in which they develop a numerical method called boundary Green's function method. In this particular paper the method is refined by the use of the Faddeev-LeVerrier algorithm.

The article demonstrates the application of the method to compute the spectral density of a 2d-half-bulk described by a tight-binding Hamiltonian.

I think that this method could be valuable to interested researchers in the field and therefore recommend publication in SciPost.

After two rounds of review I find the article to be now sufficiently clear, although in my opinion there remains room for improvement. In particular, I find the initial introduction and description of the method still too vague. It is only when looking at applications in section 4 that one develops a concrete understanding of the method.

  • validity: high
  • significance: good
  • originality: good
  • clarity: ok
  • formatting: good
  • grammar: reasonable

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