RENORMALIZATION-GROUP BLOCKING CALCULATIONS ON BOND ALTERNATION DUE TO SPIN-PEIERLS MECHANISM IN POLYACETYLENE

Abstract The real-space renormalization-group blocking (RGB) method and the extrapolated scheme are applied to a one-dimensional spin - 1 2 dimerized Heisenberg model for trans -polyacetylene (TPA) for the purpose of reinvestigating bond alternation (or dimerization) in the ground state and magnetic excitations from the standpoint of the spin-Peierls (SP) mechanism. The RGB extrapolation approach has been found to produce finite dimerizations, i.e. the stabilized SP state. The numerical estimate of the equilibrium dimerization distortion, which is found in the dimerization distortion region of the smaller of the two critical exponents of an energy gain per site, is smaller than the analytical estimate of the self-consistent harmonic approximation (SCHA). This estimate is smaller than the corresponding value observed in TPA. The barrier height of the SP dimerization potential is much smaller than the theoretical estimate of the SCHA, producing too large a population of thermally formed domain walls. Furthermore, the numerical result for the magnetic (or singlet-triplet) gap at the equilibrium geometry is consistent with the relative position between the lower covalent singlet and triplet excited states.