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Scaling behavior of the energy gap of spin-1/2 AF-Heisenberg chain in both uniform and staggered fields

We have studied the energy gap of the 1D AF-Heisenberg model in the presence of both uniform ($H$) and staggered ($h$) magnetic fields using the exact diagonalization technique. We have found that the opening of the gap in the presence of a staggered field scales with $h^ν$, where $ν=ν(H)$ is the critical exponent and depends on the uniform field. With respect to the range of the staggered magnetic field, we have identified two regimes through which the $H$-dependence of the real critical exponent $ν(H)$ can be numerically calculated. Our numerical results are in good agreement with the results obtained by theoretical approaches.