Opening of a gap in an inhomogeneous external field

We study the one-dimensional spin-1/2 antiferromagnetic Heisenberg model exposed to an external field, which is a superposition of a homogeneous field hs and a small periodic field of strength hi. For the case of a transverse staggered field a gap opens, which scales with h(1)(epsilon 1), where epsilon(1) = epsilon(1)(h(3)) is given by the critical exponent eta(1)(M(h(3))) defined through the transverse structure factor of the model at h(1) = 0. For the case of a longitudinal periodic field with wave vector q = pi/2 and strength h(q) a plateau is found in the magnetization curve at M = 1/4. The difference of the upper- and lower magnetic field scales with h(3)(u) - h(3)(l) similar to h(q)(epsilon 3), where epsilon(3) = epsilon(3)(h(3)) is given by the critical exponent eta(3)(M(h(3))) defined through the longitudinal structure factor of the model at h(q) = 0.