STRING ORDER PARAMETERS IN THE HALDANE GAP PHASE OF THE SPIN-1/2 ALTERNATING HEISENBERG CHAIN - NUMERICAL DIAGONALIZATION AND VARIATIONAL STUDY

Two possible extensions of the string order parameter originally defined for the spin-1 Heisenberg chain to the spin-1/2 alternating Heisenberg chain are examined by comparing the numerical diagonalization results of finite size systems and the variational results. It is suggested that the naive extension in which the spin-1 operator is simply replaced by the sum of two spin-1/2 operators can be regarded as the valence bond solid (VBS) order parameter while another extension proposed by Hida corresponds to the measure of the strength of the localized singlet taking the full value for the completely localized singlet state.