Ground state energy and scaling behaviour of spin gap in the XXZ spin-12 antiferromagnetic chain in longitudinal staggered field

The ground state energy and the spin gap of a spin-12 Heisenberg antiferromagnetic XXZ chain in the presence of longitudinal staggered field (hz) have been estimated by using Jordan-Wigner representation, exact diagonalization and perturbative analysis. All those quantities have been obtained for a region of anisotropic parameter (Δ) defined by 0≤Δ≤1. For Δ=0, the exact value of ground state energy is found for finite values of hz. The spin gap is found to develop as soon as the staggered field is switched on. The magnitude of spin gap is compared with the field induced gap measured in magnetic compounds CuBenzoate and Yb4As3 when Δ=1. The dependence of spin gap on both Δ and hz has been found which gives rise to scaling laws associated with hz. Scaling exponents obtained in two different cases show excellent agreements with the previously determined values. The variation of scaling exponents with Δ can be fitted with a regular function.