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Register a new userUnveiling the S=3/2 Kitaev Honeycomb Spin Liquids
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The S=3/2 Kitaev honeycomb model (KHM) has defied an analytical as well as numerical understanding because it is not exactly soluble like its S=1/2 brethren and in contrast to other spin-S Kitaev models numerical methods are plagued by a massive pile up of low energy states. Here, we uncover the phase diagram of the S=3/2 KHM and find gapped and gapless quantum spin liquids (QSLs) generally coexisting with spin quadrupolar orders. Employing an SO(6) Majorana fermion representation of spin-3/2s, we find an exact representation of the conserved plaquette fluxes in terms of static Z$_2$ gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. The latter provides an explanation for the extensive near degeneracy of low energy states in the gapless phase via the appearance of almost flat Majorana bands close to zero energy. Our parton description is in remarkable quantitative agreement with numerical simulations using the density matrix renormalization group method, and is furthermore corroborated by the addition of a single ion anisotropy which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. We discuss the implications of our findings for materials realization of higher S=3/2 KHMs and the stability of the QSL phase with respect to additional interactions.
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Motivated by recent experiments on the Kitaev honeycomb magnet $alphatext{-RuCl}_3$, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquids chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings.
We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a $mathbb{Z}_2$ spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped single-particle charge excitations are found at $mathbf{K}, mathbf{K}=(pm2pi/3, mp 2pi/3)$, with a corresponding correlation length of $xi approx 6.7$ unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language
In the field of frustrated magnetism, Kitaev models provide a unique framework to study the phenomena of spin fractionalization and emergent lattice gauge theories in two and three spatial dimensions. Their ground states are quantum spin liquids, which can typically be described in terms of a Majorana band structure and an ordering of the underlying $mathbb{Z}_2$ gauge structure. Here we provide a comprehensive classification of the gauge physics of a family of elementary three-dimensional Kitaev models, discussing how their thermodynamics and ground state order depends on the underlying lattice geometry. Using large-scale, sign-free quantum Monte Carlo simulations we show that the ground-state gauge order can generally be understood in terms of the length of elementary plaquettes -- a result which extends the applicability of Liebs theorem to lattice geometries beyond its original scope. At finite temperatures, the proliferation of (gapped) vison excitations destroys the gauge order at a critical temperature scale, which we show to correlate with the size of vison gap for the family of three-dimensional Kitaev models. We also discuss two notable exceptions where the lattice structure gives rise to gauge frustration or intertwines the gauge ordering with time-reversal symmetry breaking. In a more general context, the thermodynamic gauge transitions in such 3D Kitaev models are one of the most natural settings for phase transitions beyond the standard Landau-Ginzburg-Wilson paradigm.
Recent proposals for spin-1 Kitaev materials, such as honeycomb Ni oxides with heavy elements of Bi and Sb, have shown that these compounds naturally give rise to antiferromagnetic (AFM) Kitaev couplings. Conceptual interest in such AFM Kitaev systems has been sparked by the observation of a transition to a gapless $U(1)$ spin liquid at intermediate field strengths in the AFM spin-1/2 Kitaev model. However, all hitherto known spin-1/2 Kitaev materials exhibit ferromagnetic bond-directional exchanges. Here we discuss the physics of the spin-1 Kitaev model in a magnetic field and show, by extensive numerical analysis, that for AFM couplings it exhibits an extended gapless quantum spin liquid at intermediate field strengths. The close analogy to its spin-1/2 counterpart suggests that this gapless spin liquid is a $U(1)$ spin liquid with a neutral Fermi surface, that gives rise to enhanced thermal transport signatures.
We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the $Gamma$, $K$ and $K$ points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.
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