Quantum liquids of the S=3/2 Kitaev honeycomb and related Kugel-Khomskii models

The $S=3/2$ Kitaev honeycomb model (KHM) is unique among the spin-$S$ Kitaev models due to a massive ground state quasi-degeneracy that hampered previous numerical and analytical studies. In a recent work~\cite{jin2022unveiling}, we showed how an SO(6) Majorana parton mean-field theory of the $S=3/2$ isotropic KHM explains the anomalous features of this Kitaev spin liquid (KSL) in terms of an emergent low-energy Majorana flat band. Away from the isotropic limit, the $S=3/2$ KSL generally displays a quadrupolar order with gapped or gapless Majorana excitations, features that were quantitatively confirmed by DMRG simulations. In this paper, we explore the connection between the $S = 3/2$ KHM with Kugel-Khomskii models and discover new exactly soluble examples for the latter. We perform a symmetry analysis for the variational parton mean-field \emph{Ans{\"a}tze} in the spin and orbital basis for different quantum liquid phases of the $S=3/2$ KHM. Finally, we investigate a proposed time-reversal symmetry breaking spin liquid induced by a {[}111{]} single ion anisotropy and elucidate its topological properties as well as experimental signatures, e.g. an unquantized thermal Hall response.Comment: 17 pages, 9 figure

An Exact Chiral Amorphous Spin Liquid

Topological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.Comment: 5 pages, 3 figure