Three-Diagonal Blocks of Two-Magnon Hamiltonians with Specified Wave Numbers for Heisenberg Rings

Abstract

We demonstrate the method of creating blocks of Hamiltonian matrices for Heisenberg rings with N nodes and r = 2 overturned spins, depending on total quasimomentum k. Initial problem of dimension N 2 reduces, approximately, N -tuply, depending on N and k numbers. We consider block Hamiltonians using a particular basis, called wavelet basis. In this basis, these blocks take three-diagonal form.