Scaling behavior of the energy gap of the XXZ model in a transverse magnetic field

The energy gap of the one- dimensional ( 1D) spin-1/2 AF ( antiferromagnetic) XXZ model in a transverse magnetic field ( h) is studied by using the exact diagonalization technique. We have computed the energy gap in the region of anisotropy parameter - 1 <Delta < 1 and in the vicinity of the critical line Delta = - 1. By introducing a practical finite- size scaling approach, we have computed the correct critical exponent of the energy gap in good agreement with the field theoretical and spin- wave approaches. To check this approach, we have also studied the critical exponent of the energy gap of the 1D AF-Heisenberg chain in a staggered magnetic field ( h(s)).