Flux Fractionalization Transition in Anisotropic S=1 Antiferromagnets and Dimer-Loop Models

Abstract

We demonstrate that the low-temperature (T) properties of a class of anisotropic spin S=1 kagome (planar pyrochlore) antiferromagnets on a field-induced 13-magnetization (12-magnetization) plateau are described by a model of fully packed dimers and loops on the honeycomb (square) lattice, with a temperature-dependent relative fugacity w(T) for the dimers. The fully packed O(1) loop model (w=0) and the fully packed dimer model (w=∞) limits of this dimer-loop model are found to be separated by a phase transition at a finite and nonzero critical fugacity wc, with interesting consequences for the spin correlations of the frustrated magnet. The w>wc phase has short loops and spin correlations dominated by power-law columnar order (with subdominant dipolar correlations), while the w<wc phase has dominant dipolar spin correlations and long loops governed by a power-law distribution of loop sizes. Away from wc, both phases are described by a long-wavelength Gaussian effective action for a scalar height field that represents the coarse-grained electrostatic potential of fluctuating dipoles. The destruction of power-law columnar spin order below wc is driven by an unusual flux fractionalization mechanism, topological in character but quite distinct from the usual Kosterlitz-Thouless mechanism for such transitions: Fractional electric fluxes which are bound into integer values for w>wc, proliferate in the w<wc phase and destroy power-law columnar order. Published by the American Physical Society 2025