functions.models.BasicSquareHamiltonian

BasicSquareHamiltonian(t, p, q, k, period)[source]

The basic square lattice Hofstadter Hamiltonian.

The Hofstadter Hamiltonian for the square lattice with nearest-neighbor hopping.

Note

We have hardcoded this Hamiltonian because it is commonly used and this function is faster than calling the generic Hamiltonian method.

Parameters:

  • t (list) – The list of hopping amplitudes in order of ascending NN.

  • p (int) – The numerator of the flux density.

  • q (int) – The denominator of the flux density.

  • k (ndarray) – The momentum vector.

  • period (int) – The factor by which to divide A_UC in the flux density.

Returns:

Hamiltonian – The Hofstadter Hamiltonian matrix of dimension \(q \times q\).

Return type:

ndarray