class checkerboard_lattice_un[source]

checkerboard_lattice_un(nx, ny, t0, jax, jay, jbx, jby, v1, v2, v3, v4, beta, cell_filling, phix=0.0, phiy=0.0, cylinder=False, field=0.0, induce='nothing', border=False)

Unrestricted Hartree-Fock class to solve self-consistently the system Hamiltonian.

$$\begin{aligned} H = &-t_0\sum_{<ij>}(c_i^\dagger c_j + H.c.)+J^A_x\sum_{i\in A}(c_{i}^\dagger c_{i+x} + H.c.) +J^A_y\sum_{i\in A}(c_{i}^\dagger c_{i+y} + H.c.)\\ &+J^B_x\sum_{i\in B}(c_{i}^\dagger c_{i+x} + H.c.) +J^B_y\sum_{i\in B}(c_{i}^\dagger c_{i+y} + H.c.) +V_1\sum_{<ij>}n_in_j+V_2\sum_{<<ij>>}n_in_j\\ &+V_3\sum_{<ij>_3}n_in_j+V_4\sum_{<ij>_4}n_in_j \end{aligned}$$

Parameters

Parameters	type	Description
nx, ny	int	Number of unit cells in the x and y direction
t0, jax, jay, jbx, jby, v1, v2, v3, v4	float	Parameters of the Hamiltonian
beta	float	Inverse temperature
phix, phiy	complex	phases in x and y hoppings for twisted boundary conditions
cell_filling	float	Number of particles per 2-site unit cell. The total number of particles is then computed as cell_filling*L.
cylinder	bool	Wheter to use a cylinder geometry with open bondary conditions in the x direction.
field	float	Strength of the imaginary part of the hopping parameter across plaquettes of nearest-neighbors, which breaks time-reversal symmetry.
induce	str	Spatial pattern of the guiding field, whose strenght is determined by the field parameter.
border	bool	Wheter to include on-site chemical potentials at the open borders to avoid charge orders induced by the sharp trunctation of repulsive interactions. This parameter is irrelevant if cylinder is set to False.

Attributes

Attribute	type	Description
tre	float	Threshold of the Fermi weights to be considered non-zero Default value: 1E-10
iterations	int	Counts the number of iterations performed by the self-consistent algorithm.
etas	array of int	Stores the values of the self-consistent update parameter eta used in the iterations.
L	int	Number of two-site unit cells
L_sites	int	Number of physical sites
filling	int	Number of particles
mu	float	Value of the chemical potential in the current state of the iteration algorithm
energies	array of float	Self-consistent single-particle energies in the current state of the algorithm
energies_fermi	array of float	Self-consistent single-particle energies of the states with finite occupation in the current state of the algorithm
fermi_weigths	array of float	Fermi occupation probabilities for each of the single-particle energies in energies
total_energy	float	Expectation value of the Hamiltonian per unit cell in the current state of the algorithm
states	array of arrays of float	Matrix containing the single-particle eigenstates in the occupation basis, in the current state of the algorithm. They are ordered according to energies.
states_fermi	array of arrays of float	Matrix containing the single-particle eigenstates with finite occupation in the occupation basis, in the current state of the algorithm. They are ordered according to energies_fermi.
J_nn, J_ax, J_ay, J_bx, J_by	array of int tuples	Each element of these arrays is a tuple with the coordinates of different types of neighbors, e.g., J_nn contains the tuples with the coordinates of all nearest-neighbors. The coordinates correspond to the one-dimensional index of the flattened two-dimensional lattice.
J_nn_1, J_nn_2	array of int tuples	Decomposition of J_nn into upper diagonal and lower diagonal nearest-neighbors. This distintcion is useful for some vectorized operations.
J_nn_tw, J_ax_tw, J_ay_tw, J_bx_tw, J_by_tw	array of complex floats	Contains the hopping phases for each tuple of neighbors needed for twisted boundary conditions.
mfden	array of floats	Expected value of the Hartree-Fock self-consistent local occupation in the current step of the algorithm
mfhop_nn, mfhop_ax, mfhop_ay, mfhop_bx, mfhop_by	array of complex floats	Expected value of the Hartree-Fock self-consistent hoppings in the current step of the algorithm
mfden_0	array of floats	Initial value of the Hartree-Fock local occupation
mfhop_nn_0, mfhop_ax_0, mfhop_ay_0, mfhop_bx_0, mfhop_by_0	array of complex floats	Initial value of the Hartree-Fock hoppings
pos	array of int tuples	X and Y coordinates of each lattice site
H	L_sites x L_sites hermitian matrix of complex floats	Self-consistent Hartree-Fock Hamiltonian in the occupation basis
c_mark	array of complex float	Value of the Local Chern Marker (erase) on each unit cell of the lattice.