Quadrupolar spin liquid, octupolar Kondo coupling and odd-frequency superconductivity in an exactly solvable model

Abstract

We propose an exactly solvable model for $j_{\text{eff}}=\frac{3}{2}$ local moments on the honeycomb lattice. Our construction is guided by a symmetry analysis and by the requirement of an exact solution in terms of a Majorana fermion representation for multipole operators. The main interaction in the model can be interpreted as a bond-dependent quadrupole-quadrupole interaction. When time reversal symmetry is explicitly broken, we obtain a gapped spin liquid with a single chiral Majorana edge mode. We also investigate another solvable model in which the time-reversal-invariant spin liquid is coupled to conduction electrons in a superconductor. In the presence of a Kondo-like coupling that involves the octupole moment of the localized spins, the itinerant electrons hybridize with the emergent Majorana fermions in the spin liquid. This leads to spontaneous time reversal symmetry breaking and generates odd-frequency pairing. Our results suggest that $j_{\text{eff}}=\frac{3}{2}$ systems with strong quadrupole-quadrupole interactions may provide a route towards non-Abelian quantum spin liquids and unconventional superconductivity.

arXiv comment16 pages, 8 figures. We corrected the statement about the number of edge states in the chiral phase of the quadrupolar spin liquid. We also added the appendix B

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Cited by in corpus (12)

• Unveiling the S=3/2 Kitaev Honeycomb Spin Liquids
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
• Order Fractionalization in a Kitaev-Kondo model
• Odd-frequency pair density wave in the Kitaev-Kondo lattice model
• Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• The spin-orbital Kitaev model: from kagome spin ice to classical fractons
• Multipolar spin liquid in an exactly solvable model for $j_{\mathrm{eff}}=\frac{3}{2}$ moments
• Lieb-Schultz-Mattis constraints for the insulating phases of the one-dimensional SU($N$) Kondo lattice model
• Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction