Field-induced gap in ordered Heisenberg antiferromagnets

TL;DR

This paper investigates how a small transverse field induces an energy gap in ordered Heisenberg antiferromagnets, revealing specific scaling behaviors near quantum critical points through various analytical and numerical methods.

Contribution

It provides a detailed analysis of the field-induced gap in ordered Heisenberg antiferromagnets, including new scaling laws and critical exponents in different dimensions.

Findings

Energy gap scales as (cH)^{1/2} initially

Gap dips to (cH)^{2/3} at the quantum critical point

In 1D, the critical exponent is 4/5

Abstract

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 $h = c H$, 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 complimentary 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.