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.

arXiv comment22 pages, 7 figures

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• A Short Introduction to Topological Quantum Computation
• Projective symmetry group classification of chiral spin liquids
• Gapless chiral spin liquid in a kagome Heisenberg model
• The Spinon Fermi Surface U(1) Spin Liquid in a Spin-Orbit-Coupled Triangular Lattice Mott Insulator YbMgGaO4
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Spin Liquid versus Spin Orbit Coupling on the Triangular Lattice
• 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${}_8$
• Competing orders in pyrochlore magnets from a ${\mathbb{Z}}_2$ spin liquid perspective
• Spinon magnetic resonance of quantum spin liquids
• A classification of magnetic frustration and metamaterials from topology
• Space group symmetry fractionalization in a family of exactly solvable models with Z2 topological order
• Non-Kitaev spin liquids in Kitaev materials
• Quantum spin liquids on the diamond lattice
• Candidate quantum spin liquids on the maple-leaf lattice
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• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Even-odd effect in multilayer Kitaev honeycomb magnets