The 0's of this function occur when the desired number of particles in the system nn_ coincides with the number of particles of the system computed from the Fermi distribution that depends on the Hartree-Fock single-particle energies energies_, the chemical potential mu_, and the inverse temperature beta_. It is used to find the chemical potential of the system with the Brent's method.
This function plots bond quantities, such as the expectation value of the imaginary part of the hoppings. vecpos is an array with shape (L, 2), containing the x and y positions of the L lattice points, ordered in a one-dimensional snake-like folding. J_ is an array with shape (Lb, 2). For each of the Lb bonds that one wants to plot, it contains the two one-dimensional indeces of the sites connected by the bond, e.g., it can encode nearest-neighbors bonds. mf_ is a one-dimensional array with shape (Lb) containing the value of the quantities that one wants to plot at the Lb bonds, e.g., the iomaginary part of the nearest-neighbors hoppings expectation value.
This function plots the lattice for given position vectors posx_and posy_
This function computes the value of $V_3$ and $V_4$ for fixed $V_1$ and $V_2$, following the Rydberg dressing potential.