Projectively Implemented Altermagnetism in an Exactly Solvable Quantum Spin Liquid

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 Z_{2} quantum spin(-orbital) liquids (QSLs), which simultaneously support magnetic long-range order as well as fractionalization and Z_{2} topological order. Our symmetry analysis reveals that in this model three distinct types of "fractionalized altermagnets (AM^{*})" emerge, which can be distinguished by their residual symmetries. Importantly, the fractionalized excitations of these states carry an emergent 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.