Generalized String Order in the Spin-1/2 Alternating Heisenberg Chain

抄録

The phase-dependent generalized string order introduced by Oshikawa in the VBS (valence bond solid)-type states of the integer spin chain is extended to the spin-1/2 J−J′ alternating Heisenberg chain with antiferromagnetic J. The numerical diagonalization and the bosonization analysis show that the generalized string order remains finite in the ground state of the present model for −∞<J′<J, taking the maximum at J′=0. The characteristic feature of the phase dependence of the generalized string order also coincides with that of the spin-1 VBS state. This reconfirms the notion that the Haldane state of the spin-1 chain and the dimerized state of the alternating chain belong to a single phase characterized by the local singlet-type correlation.