Breakdown of the Spin-1 Haldane Phase Via Quantum Fluctuations

Abstract

Investigating quantum fluctuations in the ground states of S=1 quantum antiferromagnetic spin chains described by the bilinear-biquadratic Hamiltonian ℋ=∑i [Si·Si+1+β (Si·Si+1)2], 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 β < 1/3, the minimization of the variational energy results in a bound state of crackions, while at β > 1/3, crackions come to be set free from their bound state with increase of β and the chain length. We point out that the breakdown of the Haldane phase with β approaching 1 can be attributed to the collapse of the bound state and the growth of a short-range repulsive interaction between crackions.