Quantum Fluctuations to Cause the Breakdown of the Spin-1 Haldane Phase

Investigating quantum fluctuations in the ground states of S=1 quantum antiferromagnetic spin chains described by the bilinear-biquadratic Hamiltonian, we study a mechanism of the breakdown of the Haldane phase. Based on the valence-bond-solid structure, but replacing two links of them by triplet bonds (crackions), we construct a trial wave function which is singlet and translationally invariant, where the crackion-crackion distance is regarded as a variational parameter. At $\beta<1/3$, the minimization of the variational energy results in a bound state of crackions, while at $\beta>1/3$, crackions come to be set free from their bound state with increase of $\beta$ and the chain length. We point out that the breakdown of the Haldane phase with $\beta$ approaching 1 can be attributed to the collapse of the bound state and the growth of a short-range repulsive interaction between crackions.