Crossover between the Haldane-gap phase and the dimer phase in the spin-1/2 alternating Heisenberg chain

The ground-state properties of the spin-1/2 Heisenberg chain, which has two exchange couplings (J>J’) alternatingly, are studied. This model interpolates the spin-1 antiferromagnetic Heisenberg chain (AFHC) (J’→-∞, J>0), the dimerized spin-1/2 AFHC (J’≃J>0), and the uniform spin-1/2 AFHC (J’=J>0) continuously. The string order introduced by den Nijs–Rommelse and Tasaki changes continuously through the Haldane phase and the dimer phase to vanish at J=J’. It is at a maximum for J’=0. This implies that the string order is related to the local singlet correlation in terms of the spin-1/2 model. The lowest excitation can be regarded as the renormalized triplet wave. The reversal of the anisotropy effect on the excitation spectrum of the spin-1 AFHC is also explained in a intuitive way based on this picture.