Amp\`ere phase in frustrated magnets

TL;DR

This paper introduces a new class of algebraic spin liquids called Ampère phases, characterized by curl-based constraints and vectorial magnetic excitations, expanding understanding of frustrated magnet systems.

Contribution

The paper identifies and analytically characterizes Ampère phases as a novel class of algebraic spin liquids with curl-based local constraints and unique magnetic excitations.

Findings

Ampère phases exhibit power-law magnetic correlations with an exponent equal to the space dimension.

Monte Carlo simulations confirm the existence and properties of Ampère phases in 2D and 3D.

Ampère phases differ from Coulomb spin liquids by having vectorial magnetic loops instead of monopoles.

Abstract

We report a new class of algebraic spin liquids, in which the macroscopically degenerate ground state manifold is not Coulombic, like in spin ices, but Amp\`ere-like. The local constraint characterizing an Amp\`ere phase is not a Gauss law, but rather an Amp\`ere law, i.e., a condition on the curl of the magnetization vector field and not on its divergence. As a consequence, the excitations evolving in such a manifold are not magnetically charged scalar quasiparticles, the so-called magnetic monopoles in Coulomb phases, but instead vectorial magnetic loops (or fictional current lines). We demonstrate analytically that in a macroscopically degenerate manifold inheriting the properties of a cooperative paramagnet and subject to a local curl-free contraint, magnetic correlations decay in space with a power law whose exponent is the space dimension d: the Amp\`ere phase is a d-algebraic spin liquid. Using Monte Carlo simulations with appropriate cluster dynamics, we confirm this physics numerically in two- and three-dimensional examples, and illustrate how the Amp\`ere phase compares to its Coulomb counterpart.