qat.fermion.hamiltonians.make_hubbard_model
- qat.fermion.hamiltonians.make_hubbard_model(t_mat: ndarray, U: float, mu: float) ElectronicStructureHamiltonian
Constructs Hubbard model
\[H = \sum_{ij,\sigma} (t_{ij} - mu \delta_{ij}) c^\dagger_i c_j + U \sum_i n_{i\uparrow} n_{i \downarrow}\]- Parameters
t_mat (np.ndarray) – Hopping matrix (n_sites x n_sites). t_mat may have diagonal terms contributing to the chemical potential on each site.
U (float) – Hubbard U.
mu (float) – Reference chemical potential.
- Returns
The Hubbard Hamiltonian.
- Return type
Notes
Spin-orbital labeling convention: \(i \equiv (k, \sigma) = 2 k + \sigma\) with \(i\): site index and \(\sigma\): spin index.