The method of exact diagonalization preserving the total spin and taking the point symmetry of the two-dimensional isotropic Heisenberg magnet into account

We propose a double-pass method of exact diagonalization of a finite cluster on the base of functions that have a definite total spin and transform by a definite irreducible representation of the point symmetry group of the lattice. We also propose the method for approximating the energy spectrum in the thermodynamic limit using the spectrum of the surrounding states, which increases the calculation accuracy leaving the cluster size invariant. The algorithm details are extensively illustrated with an example of clusters of spin $1/2$ on a simple square lattice.