Real-space renormalization group with effective interactions

The real-space renormalization group for the study of periodic systems goes through the reduction of the Hilbert space to products of lowest eigenstates of identical blocks. Instead of working with the Hamiltonian, it is possible to estimate effective interactions between blocks from the spectrum of dimers or trimers of blocks, according to the effective Hamiltonian theory of Bloch. Tests on a series of spin problems [cohesive energy of the one-dimensional (1D) chain and of the 2D square lattice, excitation energies of the dimerized 1D spin chain, and behavior of the frustrated chain in the low frustration regime] show the potentiality of the method.