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Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer of an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction, J, is analyzed through Abrikosov fermion mean-field theory. The system sustains quantum spin liquid (QSL) solutions which have different character depending on parity of the number of layers. While in even layered Kitaev models a gapped QSL emerges, odd-layered models host gapless QSLs. The projective symmetry group analysis of these solutions unravel a layer-to-layer inversion symmetry rather than an expected reflection. Although these QSLs retain features of the single layer Kitaev spin liquid (KSL), they should be regarded hybrid QSLs consisting on several KSLs. The good agreement at large-J between the energy of the Gutzwiller projected mean-field QSL and the exact energy indicates that such QSL Ansatz is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of alpha-RuCl3 and H3LiIr2O6 which are examples of magnetically coupled multilayer Kitaev models., Comment: 16 pages, 8 figures

Motivated by the possibility of finding a bosonic quantum spin liquid in the integer spin-$S$ Heisenberg-Kitaev model on the honeycomb lattice, we derive a Schwinger boson mean field theory involving both singlet and triplet pairing channels which includes hopping and pairing operators on equal footing. The mixed construction introduced here is justified by the good comparison with exact diagonalization energies of the $S \leq 3/2$ Heisenberg-Kitaev model and the perfect match with the Luttinger-Tisza semiclassical energies obtained at large-$S$. We find various competing gapped quantum spin liquids close to the Kitaev point. A comparison of their spin excitation spectrum with the dynamical structure factor obtained from exact diagonalizations allows us to identify the physical spin liquid $ans\"atz$ of the model. In particular, we identify a chiral quantum spin liquid state whose spin excitation spectrum follows closely the exact diagonalization data and survives up to large spin $S \lesssim 2$. We propose this state as a promising quantum spin liquid candidate for the integer spin-$S$ antiferromagnetic Kitaev model which may be realized in $S=1$ Kitaev materials A$_3$Ni$_2$XO$_6$ and KNiAsO$_4$., Comment: 13 pages, 11 figures

$\require{mhchem}$The square-kagome lattice Heisenberg antiferromagnet is a highly frustrated Hamiltonian whose material realizations have been scarce. We theoretically investigate the recently synthesized $\ce{Na6Cu7BiO4(PO4)4Cl3}$ where a Cu$^{2+}$ spin-$1/2$ square-kagome lattice (with six site unit cell) is decorated by a seventh magnetic site alternatingly above and below the layers. The material does not show any sign of long-range magnetic order down to 50 mK despite a Curie-Weiss temperature of $-212$ K indicating a quantum paramagnetic phase. Our DFT energy mapping elicits a purely antiferromagnetic Hamiltonian that features longer range exchange interactions beyond the pure square-kagome model and, importantly, we find the seventh site to be strongly coupled to the plane. We combine two variational Monte Carlo approaches, pseudo-fermion/Majorana functional renormalization group and Schwinger-Boson mean field calculations to show that the complex Hamiltonian of $\ce{Na6Cu7BiO4(PO4)4Cl3}$ still features a nonmagnetic ground state. We explain how the seventh Cu$^{2+}$ site actually aids the stabilization of the disordered state. We predict static and dynamic spin structure factors to guide future neutron scattering experiments., Comment: 5 pages, 4 figures. Supplement: 7 pages, 11 figures v2: minor revisions in text and figure labels

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus., Comment: Last version before publication in PRB

The large thermal Hall conductivity recently detected in Mott insulating cuprates has been attributed to chiral neutral spin excitations. A quantum spin liquid with Majorana excitations, Chern number +/-4 and large thermal Hall conductivity is found to be an excited state of a frustrated Heisenberg model on the square lattice. Using a Majorana mean-field theory and exact diagonalizations, we explore two possible routes to achieve this chiral quantum spin liquid, an orbital effect of an applied magnetic field and spin orbit couplings as present in cuprates. In particular, we show how only the orbital magnetic field allows this topological phase to be the ground state, while it remains an excited state of the Majorana mean field under the Dzyaloshinskii-Moriya terms. We interpret the large thermal Hall effect observed in Mott cuprates from their close proximity to a transition to a Majorana chiral quantum spin liquid which can be induced by an external magnetic field., Comment: 6 pages, 4 figures + supplemental material