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

TL;DR

This paper maps out the phase diagram of a bond-alternating S=1/2 quantum spin chain, revealing various phases including the Haldane phase, using series expansions to analyze ground state properties.

Contribution

It provides the first detailed phase diagram of the bond-alternating S=1/2 quantum spin chain, highlighting the different symmetry-breaking phases and their relation to the parameters.

Findings

Identification of multiple ground state phases including the Haldane phase.

Characterization of symmetry-breaking and non-breaking phases.

Use of series expansions to determine the phase boundaries.

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 +\lambda S_{2j}^z S_{2j+1}^z ) +\beta \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 $S=1 \ XXZ$ 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.