Altermagnets are a new class of symmetry-compensated magnets with large spin splittings. Here, we show that the notion of altermagnetism extends beyond the realm of Landau-type order: we study exactly solvable ${\mathbb{Z}}_2$ quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and ${\mathbb{Z}}_2$ topological order. Our symmetry analysis reveals that in this model three distinct types of “fractionalized altermagnets (${\text{AM}}^{*}$)” emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent ${\mathbb{Z}}_2$ gauge charge, which implies that they transform projectively under symmetry operations. Consequently, we show that “altermagnetic spin splittings” are now encoded in a momentum-dependent particle-hole asymmetry of the fermionic parton bands. We discuss consequences for experimental observables such as dynamical spin structure factors and (nonlinear) thermal and spin transport.

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• Altermagnetism
• Fractionalization
• Quantum spin liquid
• Altermagnets
• Lattice gauge theory
• Projective symmetries