Amp\`ere phase in frustrated magnets

N. Rougemaille; J. Coraux; B. Canals

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arXiv · 2501.08859

Amp\`ere phase in frustrated magnets

N. Rougemaille·J. Coraux·B. Canals

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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.

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N. Rougemaille, J. Coraux, B. Canals. 2025-01-15. Amp\`ere phase in frustrated magnets. https://arxiv.org/abs/2501.08859

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