Perturbation theory by flow equations: dimerized and frustrated S=1/2 chain

The flow equation method (Wegner, 1994) is used as continuous unitary transformation to construct perturbatively effective Hamiltonians. The method is illustrated in detail for dimerized and frustrated antiferromagnetic S = 1/2 chains. The effective Hamiltonians conserve the number of elementary excitations which are S = 1 magnons for the dimerized chains. The sectors of different; number of excitations are clearly separated. Easy-to-use results for the gap, the dispersion and the ground state energies of the chains are provided.