Classification of spin liquids on the square lattice with strong spin-orbit coupling

Abstract

Spin liquids represent exotic types of quantum matter that evade conventional symmetry-breaking order even at zero temperature. Exhaustive classifications of spin liquids have been carried out in several systems, particularly in the presence of full SU(2) spin-rotation symmetry. Real magnetic compounds, however, generically break SU(2) spin symmetry as a result of spin-orbit coupling - which in many materials provides an `order one' effect. We generalize previous works by using the projective symmetry group method to classify $Z_2$ spin liquids on the square lattice when SU(2) spin symmetry is maximally lifted. We find that, counterintuitively, the lifting of spin symmetry actually results in vastly more spin liquid phases compared to SU(2)-invariant systems. A generic feature of the SU(2)-broken case is that the spinons naturally undergo $p+ip$ pairing; consequently, many of these $Z_2$ spin liquids feature a topologically nontrivial spinon band structure supporting gapless Majorana edge states. We study in detail several spin-liquid phases with varying numbers of gapless edge states and discuss their topological protection. The edge states are often protected by a combination of time reversal and lattice symmetries and hence resemble recently proposed topological crystalline superconductors.

22 pages, 7 figures

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Cited by in corpus (10)

• Magnons and Excitation Continuum in XXZ triangular antiferromagnetic model: Application to $B{a}_{3}CoS{b}_2{O}_9$
• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
• Spinon magnetic resonance of quantum spin liquids
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Non-Kitaev spin liquids in Kitaev materials
• Candidate quantum spin liquids on the maple-leaf lattice
• Quantum spin liquids on the diamond lattice
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Even-odd effect in multilayer Kitaev honeycomb magnets