Ground state of an Ising-type spin-1/2 chain with competing interactions

The ground state of an Ising-type spin-1/2 chain with ferromagnetic bond-alternating nearest-neighbor and anti-ferromagnetic uniform next-nearest-neighbor interactions is studied by using the exact-diagonalization method and the density-matrix renormalization-group method. The Hamiltonian describing the system is expressed as H=– (Sigma) h2i–1,2i – J1 (Sigma) h2i,2i+1 + J2 (Sigma) hi,i+2 with hi,iʹ=g(Six Siʹx + Siy Siʹy) + Siz Siʹz, where J1 >=0, J2 >=0, and 1 > (gamma) >=0. Special attention is paid to the groundstate phase diagram on the J1 versus J2 plane for a given value of (gamma). The phase diagram is composed of the ferromagnetic, intermediate, and up-up-down-down phases, the intermediate phase being characterized by its magnetization, which takes finite but unsaturated values. The phase diagram obtained for (gamma)=0.5 shows that the region of the intermediate phase for a given value of J1 is widest when J1=1.0 and becomes narrower rather rapidly as J1 decreases or increases from 1.0. The J2-dependence of the ground-state magnetization for (gamma)=0.5 and J1=0.85 is also discussed.