Phase diagram of the S=1/2 quantum spin chain with bond alternation

Abstract

We study the ground state properties of the bond alternating $S=1/2$ quantum spin chain whose Hamiltonian is H=\sum_j (S_{2j}^x S_{2j+1}^x +S_{2j}^y S_{2j+1}^y +λS_{2j}^z S_{2j+1}^z ) +β\sum_j {\bf S}_{2j-1} \cdot {\bf S}_{2j} . When $\beta =0$, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling $\beta \to -\infty$, this is equivalent to the $S=1XXZ$ Hamiltonian. It has several ground state phases in the $\lambda$-$\beta$ plane including the gapful Haldane phase. They are characterized by a full breakdown, partial breakdowns and a non-breakdown of the hidden discrete $Z_2\times Z_2$ symmetry. The ground state phase diagram is obtained by series expansions.

25 pages, RevTex 2.0, 9 Figures available on request, Tec.rep. of ISSP No.A2652

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