Ab initio analysis of the topological phase diagram of the Haldane model

TL;DR

This paper performs an ab initio analysis of a Hamiltonian that maps to the Haldane model, accurately computing tunnelling coefficients and the phase diagram, revealing limitations in accessing the topological phase.

Contribution

It introduces two independent methods to compute tunnelling coefficients and maps the phase diagram of the Haldane model from a continuous Hamiltonian.

Findings

Accurate reproduction of the spectrum using Wannier functions and gauge-invariant spectrum properties.

Identification that the topological insulator phase is suppressed in deep tight-binding regimes.

Limited access to the original Haldane phase diagram in practical parameter ranges.

Abstract

We present an ab initio analysis of a continuous Hamiltonian that maps into the celebrated Haldane model. The tunnelling coefficients of the tight-binding model are computed by means of two independent methods - one based on the maximally localized Wannier functions, the other through analytic expressions in terms of gauge-invariant properties of the spectrum - that provide a remarkable agreement and allow to accurately reproduce the exact spectrum of the continuous Hamiltonian. By combining these results with the numerical calculation of the Chern number, we are able to draw the phase diagram in terms of the physical parameters of the microscopic model. Remarkably, we find that only a small fraction of the original phase diagram of the Haldane model can be accessed, and that the topological insulator phase is suppressed in the deep tight-binding regime.