Field-induced gap in ordered Heisenberg antiferromagnets

Heisenberg antiferromagnets in a strong uniform magnetic field H are expected to exhibit a gapless phase with a global O(2) symmetry. In many real magnets, a small energy gap is induced by additional interactions that can be viewed as a staggered transverse magnetic field h=cH, where c is a small proportionality constant. We study the effects of such a perturbation, particularly for magnets with long-range order, by using several complementary approaches: numerical diagonalizations of a model with long-range interactions, classical equations of motion, and scaling arguments. In an ordered state at zero temperature, the energy gap at first grows as (cH)(1/2) and then may dip to a smaller value, of order (cH)(2/3), at the quantum critical point separating the "gapless" phase from the gapped state with saturated magnetization. In one spatial dimension, the latter exponent changes to 4/5.