Haldane Model

This UI interface allows for continuous control of the parameters in Haldane's quantum anomalous Hall model. Both the Fermi surface, band dispersion, and Berry curvature for the upper and lower bands are calculated and updated interactively in real-time.

Click the "Launch" button to access the main panel displaying various quantities from the Haldane model.

Additionally, there are two other buttons:

1. Clicking "A(k,ω)" will calculate the 3D spectral function of the Haldane bands and display it using the 3D smart displayer (refer to the manual from a recent project for more details).
2. Clicking "Ω(k)" will compute the Berry curvature of both bands individually. We offer two numerical methods for this calculation, with the second method potentially providing higher efficiency under certain circumstances.

In the main panel, the definition of the parameters "t1" "t2" "m" and "phi" can be find in Haldane's paper, which control the electronic structure as well as topological invariant.

The control variable "Im{Σ}" represents the imaginary part of the self-energy in the spectral function and contributes to the spectral weight displayed in the upper plots.

If the control variable "update" is set to 1 (or 0), tuning Haldane's parameters will (or will not) automatically update the Berry curvatures shown in the lower panels.

The control variable "HQ" controls the grid resolution for Berry curvature calculations. Setting HQ = 0 uses a coarse grid for faster calculations, while HQ = 1 results in a finer grid, producing smoother data but taking longer.

Additionally, we automatically calculate the Chern number by integrating the Berry curvature across the Brillouin zone, displaying the Chern number for each band.

Ref. Duncan Haldane Phys. Rev. Lett. 61 (1988) 2015-2018