functions.models.diag_func

diag_func(t_val, p_val, q_val, A_UC_val, vec_group, k_val, dJ_val, J_idx_val)

The diagonal function.

The function that populates the diagonals of the Harper matrix is given by

$$\begin{gathered} \begin{array}{r}{\mathrm{\Lambda }}_{l,n}=-\sum _{\kappa }\sum _{⟨ij{⟩}_{\kappa }^l}{t}_{\kappa }{e}^{ \\ \mathrm{i}{\theta }_{ij}}{e}^{ \\ \mathrm{i} \\ \mathbf{k}\cdot \\ \mathbf{r}},\end{array} \end{gathered}$$

where $⟨\dots {⟩}_{\kappa }^l$ denotes the subset of $\kappa$-th nearest neighbors with a net $y$ unit cell displacement of $l$, ${\theta }_{ij}$ is the Peierls phase, $\mathbf{k}$ is the momentum vector, and $\mathbf{r}$ is the displacement vector.

Parameters:

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

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

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

• A_UC_val (float) – The unit cell area in units of a2 (possibly scaled by a periodicity factor).

• vec_group (ndarray) – The array of relevant nearest neighbors grouped by dJ.

• k_val (ndarray) – The momentum vector.

• dJ_val (int) – The y-displacement in terms of unit cells.

• J_idx_val (int) – The y-position in terms of unit cells.

Returns:

term – The diagonal term.

Return type:

complex