Three-dimensional spin-orbital liquids

Abstract

Spin-orbital liquids provide an exactly solvable route to three-dimensional Z2 quantum spin liquids beyond the original Kitaev setting. Built from higher-dimensional Clifford-algebra representations, spin-orbital Hamiltonians can be realized on both three- and four-coordinated lattices, giving rise to phases with 3 and 2 itinerant Majorana flavors, respectively. We demonstrate that these models host a rich set of gapless Majorana metals, characterized, in particular, by topological Fermi surfaces, nodal lines, and Weyl semimetal phases. We analyze the stability of these structures under physically motivated perturbations and identify generic splitting patterns and topological transitions driven by symmetry breaking and flavor mixing. This yields a unified organizing framework for three-dimensional Majorana metals in fractionalized spin liquids.