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Three-dimensional spin-orbital liquids

Anna Sandberg1, Lukas Rødland2, and Maria Hermanns1,*

  • *Contact author: maria.hermanns@fysik.su.se
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Phys. Rev. B 113, 235120 – Published 12 June, 2026

DOI: https://doi.org/10.1103/qhfj-m9dl

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 ν=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.

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Phys. Rev. B 113, 235120– Published 12 June, 2026
  • Received 16 February 2026
  • Revised 21 April 2026
  • Accepted 19 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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