liebTB code¶

liebTB module models a line centered squared lattice (Lieb lattice) with real and/or complex valued hoppings and onsite energies.

liebTB is available at https://github.com/cpoli/TB

class liebTB.eigLieb(lat)[source]¶

Child of the class eigTB. Dedicated to the Lieb lattice.

set_hop_alt(ta, tb, tc, td)[source]¶

Get the nearest hoppings of the Lieb lattice with alternating hoppings and, the next nearest hoppings. As the next nearest hoppings are diagonal hoppings, the value of the diagonal between $t_1$ and $t_2$ is given by $c\sqrt{t_1^2+t_2^2}$ .

Parameters:	ta – Value of the math:t_{ab} hoppings. tb – Value of the math:t_{ba} hoppings. tc – Value of the math:t_{ac} hoppings. td – Value of the math:t_{ca} hoppings.

set_hop_alt_nn(nn)[source]¶

Get the next nearest hoppings if the Lieb lattice has alternating hoppings.

Parameters:	c – Strength of the diagonal hoppings.

set_dim_defect(dim_x=-1, dim_y=-1)[source]¶

Set dimerization defects along $x$ and/or $y$ .

Parameters:	dim_x – Default value -1 (no defect). Dimerization along $x$ site index. dim_x – Default value -1 (no defect). Dimerization along $y$ site index.

set_disorder_uniform(alpha)[source]¶

Set a non generic disorder. Disorder uniform along math:y for math:t_{ab} and math:t_{ba}, and uniform along math:x for math:t_{ac} and math:t_{ca}.

Parameters:	alpha – Stength of the disorder.

Note

This disorder preserves the zero mode.

set_disorder_pair(alpha)[source]¶

Set a non generic disorder.

Parameters:	alpha – Stength of the disorder.

Note

This disorder preserves the zero mode.

set_disorder_placket(alpha)[source]¶

Set a non generic disorder.

Parameters:	alpha – Stength of the disorder.

Note

This disorder preserves the zero mode.

set_magnetic_field(theta)[source]¶

Add Pierls phases to the hoppings.

Parameters:	nx – Number of sites along math:x. (Input of the class latticeTB)

Note

This disorder preserves the zero mode.

get_butterfly(N)[source]¶

‘ Get energies depending on phase.

Parameters:	N – Number of spectra.

class liebTB.plotLieb(sys)[source]¶

Plot the output of the class latticeTB and the class eigTB.

plt_lattice_hop(ms=20, lw=1)[source]¶: Plot the coordinates of the Lieb lattice sites in hoppings space. :param hop: Hoppings. :param nx: Number of sites along $x$ . :param ny: Number of sites along $y$ . :param ms: Default value 20. Markersize.

plt_dispersion(ta, tb, tc, td, nn=0.0, fs=20, N=100)[source]¶

Plot the relation dispersion of the Lieb lattice.

Parameters:	ta – Hoppings. nx – Number of sites along $x$ . ny – Number of sites along $y$ . ms – Default value 20. Markersize.

liebTB.equations(p, param)[source]¶: Get the intersection of the points at the extremity of two segments. Used to build up the lattice in hopping space.