Effects of Charge Ordering on Spin-Wave of Quarter-Filled   Spin-Density-Wave States
  Spin-wave excitations of quarter-filled spin-density-wave state, which coexists with charge ordering, have been studied for one-dimensional extended Hubbard model with the nearest-neighbor repulsive interaction (V) and next-nearest-neighbor one (V_2). We calculate dispersion relations for the acoustic and optical spin-wave within the random phase approximation. Our numerical calculation shows that energy spectrum of the acoustic branch is well described by a simple sine function form. In the states coexisting with charge-density-wave, the spin-wave velocity decreases with increasing V or V_2. Our numerical result, that velocity reduces to zero in the limit of large V or V_2, is analyzed in terms of a spin 1/2 Heisenberg model with effective antiferromagnetic exchange interaction. 
Y. Tomio, Y. Kurihara and Y. Suzumura