calc_n

hubbard.calc_n(H, q)[source]

General method to obtain the spin densities for periodic or finite systems at a given temperature

It obtains the spin densities from the direct diagonalization of the Hamiltonian (H.H) taking into account a possible overlap matrix (H.H.S):

\[\langle n_{i\sigma} \rangle = \sum_{\alpha}f_{\alpha\sigma}\sum_{j}c^{\alpha}_{i\sigma}c^{*\alpha}_{j\sigma}S_{ij}\]

Where \(f_{\alpha\sigma}\) is the weight of eigenstate \(\alpha\) for spin \(\sigma\) at temperature kT (Fermi-Dirac distribution), \(c^{\alpha}_{i\sigma}\) are coefficients for eigenstate \(\alpha\) with spin \(\sigma\) represented in the basis of atomic orbitals

Parameters

H (HubbardHamiltonian) – hubbard.HubbardHamiltonian object of the system to obtain the spin-densities from
q (array_like) – charge resolved in spin channels (first index for up-electrons and second index for down-electrons)