Hydrogen chain#

One of the simplest models to check that the code is working properly. We consider a linear chain of atoms with \(s\) orbitals only. Do note that the SK amplitude used for these s orbitals does not actually correspond to any hydrogen calculation. The band structure can be obtained analitically in this case:

\[\varepsilon(k) = \varepsilon_0 - 2t\cos{ka}\]

where \(\varepsilon_0\) is the onsite energy, and \(t\) the hopping amplitude (amplitude for \(s\) orbital in the SK context). The band structure as obtained with the configuration file is:

../../_images/chain_bands.png

Note that we need to include spin in the model to achieve half-filling; if we were to consider only one orbital (spinless) then the resulting system would have to be either empty of full, since the number of electrons per unit cell must be an integer. The configuration file is:

examples/chain.txt#
SystemName: Test chain
Dimensions: 1
Lattice:
  - [1.0, 0.0, 0.0]
Species: H
Motif:
  - [0.0, 0.0, 0.0, 0]
Filling: 1
Orbitals: s
OnsiteEnergy:
  - 1
SKAmplitudes:
  - (0, 0) -0.3
Spin: True
SOC: 0
Mesh: 200
SymmetryPoints: K G K