3D Spin-orbital liquids

TL;DR

This work develops and analyzes 3D spin–orbital liquids (SOLs) built from higher-dimensional Clifford algebra representations, yielding exactly solvable models with multiple Majorana flavors. On three- and four-coordinated lattices, SOLs realize gapless Majorana metals with topological Fermi surfaces, nodal lines, and Weyl points, whose existence and stability are governed by lattice symmetries, projective symmetry implementations, and flavor mixing. By systematically classifying perturbations that preserve solvability, the authors map out how TR, flavor, and lattice symmetries reorganize nodal manifolds—demonstrating robust topological phases and transitions across representative 3D lattices: Hyperoctagon, Hyperhoneycomb, Hyperhexagon (ν=3) and Chiral square-octagon, Layered honeycomb (ν=2). The results provide a unified framework for 3D Majorana metals in fractionalized spin liquids and establish a platform for exploring surface states, dynamical probes, and flux-pattern stability in realistic settings. The analysis clarifies how flavor structure and symmetry constraints shape universal features of 3D SOLs, guiding future studies of interacting instabilities and experimental signatures in correlated spin systems.

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. 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.

Figures (25)

• Figure 1: Local choice of sublattice for the Klein rotation.
• Figure 2: Hyperoctagon lattice with unit cell and translation vectors. Colors blue/purple/pink denote $x$/$y$/$z$-bonds.
• Figure 3: (a) BZ and FSs for the unperturbed SOL on the hyperoctagon lattice. (b)-(e) High-symmetry line plots for the unperturbed model, as well as for switching on one of the perturbations.
• Figure 4: Phase diagram for NN perturbations on the hyperoctagon lattice, where only one of the TR invariant perturbations $\Gamma$, $\Gamma'$, and $K$ is changed. $r_j$ denotes the $j$th root of $(1-12\Gamma'^2-8\Gamma'^3+4\Gamma'^4+16\Gamma'^5+16\Gamma'^6)$.
• Figure 5: Hyperhoneycomb lattice with unit cell and translation vectors. Colors blue/purple/pink denote $x$/$y$/$z$-bonds.