Perfect deporalization of the Loudon-Fleury inelastic visible-light scattering in the Kitaev honeycomb model is well known. Though it happens in Heisenberg Kagome and triangular antiferromagnets as well, yet we prove it to be of geometric origin rather than peculiar to quantum spin liquids. A Kitaev spin liquid in the square planar geometry indeed exhibits polarized Raman spectra containing defferent symmetry species, each brought by symmetry-compatible spinon geminate excitations, i.e. arising from symmetry-compatible direct-product representations made of double-valued irreducible representations of mediating-spinon-belonging gauged
k-point symmetry groups. We combine a standard point-symmetry-group analysis of the Raman vertex in the real space and an elaborate projective-symmetry-group analysis of Raman-scattering-mediating Majorana spinons in the reciprocal space to identify emergent spinons singly.
Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities do not reflect the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.
Abstract We study magnetic Raman, i.e. inelastic light, scattering of Kitaev’s quantum spin liquids realizable in honeycomb nanoribbons. Elementary excitations in the Kitaev spin liquids consist of itinerant Majorana (matter) fermions and localized gauge fluxes (visons). Matter fermions are characterized by the projective point (gauged rotation) group inherent in the lattice. Inelastic light scattering is mediated by a pair of matter fermions without any vison excitation. We can selectively “observe” matter fermions of the same symmetry and those of different symmetries depending on the polarization of incoming and/or outgoing lights. A pair of matter fermions with particular translational quantum numbers ±k cannot be Raman active.
Abstract We demonstrate a Kitaev spin liquid in a polyhedral cluster and propose detecting its fractional excitations—Majorana spinons—by magnetic Raman scattering. While little polarization dependence of the Raman spectra at sufficiently low temperatures is usual with quantum spin liquids, the present observations are primarily of geometric origin. The Raman scattering intensity peaks melt with increasing temperature, to be more precise, with increasing number of background gauge-flux excitations.
We revisit the fermionic parton approach to
S=1/2 quantum spin liquids with
SU(2) spin-rotation symmetry, and the associated projective symmetry group (PSG) classification. We point out that the existing PSG classification is incomplete; upon completing it, we find spin-liquid states with
S=1 and
S=0 Majorana fermion excitations coupled to a deconfined
Z2 gauge field. The crucial observation leading us to this result is that, like space group and time-reversal symmetries, spin rotations can act projectively on the fermionic partons; that is, a spin rotation may be realized by simultaneous
SU(2) spin and gauge rotations. We show that there are only two realizations of spin rotations acting on fermionic partons: the familiar naive realization where spin rotation is not accompanied by any gauge transformation, and a single type of projective realization. We discuss the PSG classification for states with projective spin rotations. To illustrate these results, we show that there are four such PSGs on the two-dimensional square lattice. We study the properties of the corresponding states, finding that one---with gapless Fermi points---is a stable phase beyond mean-field theory. In this phase, depending on parameters, a small Zeeman magnetic field can open a partial gap for the Majorana fermion excitations. Moreover, there are nearby gapped phases supporting
Z2 vortex excitations obeying non-Abelian statistics. We conclude with a discussion of various open issues, including the challenging question of where such
S=1 Majorana spin liquids may occur in models and in real systems.
We perform extensive classifications of
Z2 quantum spin liquids on the simple cubic, body centered cubic, and face centered cubic (fcc) lattices using a spin-rotation-invariant fermionic projective symmetry group approach. Taking into account that all three lattices share the same point group
Oh, we apply an efficient gauge where the classification for the simple cubic lattice can be partially carried over to the other two lattices. We identify hundreds of projective representations for each of the three lattices, however, when constructing short-range mean-field models for the fermionic partons (spinons) these phases collapse to only very few relevant cases. We self-consistently calculate the corresponding mean-field parameters for frustrated Heisenberg models on all three lattices with up to third-neighbor spin interactions and discuss the spinon dispersions, ground-state energies, and dynamical spin structure factors. Our results indicate that phases with nonuniform spinon hopping or pairing amplitudes are energetically favored. An unusual situation is identified for the fcc lattice where the spinon dispersion minimizing the mean-field energy features a network of symmetry-protected linelike zero modes in reciprocal space. We further discuss characteristic fingerprints of these phases in the dynamical spin structure factor which may help to identify and distinguish them in future numerical or experimental studies.