Projective symmetry group classification of fermionic
Z2 spin liquids on the dipolar-octupolar pyrochlore magnets
We construct and classify
Z2 quantum spin liquids (QSLs) of fermionic partons on the dipolar-octupolar (DO) pyrochlore lattice. The DO pseudospin shares the space-group and time-reversal algebra of the effective spin-1/2 Kramers doublet, its projective symmetry group (PSG) yields the same 48 symmetric
Z2 classes as the generic fermionic classification. We show, the distinct DO symmetry action, encoded in a set of sublattice-independent operators, selects a physically different set of symmetry-allowed mean-field channels, so that the resulting ansatze, spinon spectra, and observables differ from both the effective spin-1/2 case and the bosonic DO classification. Decomposing the anisotropic XYZ exchange model into all symmetric singlet and triplet hopping and pairing channels and minimizing the mean-field energy self-consistently, we obtain phase diagrams in the (
Jx~,Jz~) plane in which only a few
Z2 states, several supporting gapless or flat-band spinon spectra, are stabilized. For these states we compute the spinon band structures, the low-temperature specific heat, and the dynamical spin structure factor, and we argue that the power-law specific-heat exponent is a diagnostic of the spinon nodal structure. A near-linear-in-temperature specific heat together with broad continua in the structure factor gives a fermionic-parton account of the gapless, fractionalized thermodynamics reported in DO materials such as
Nd2ScNbO7, complementing the bosonic quantum-spin-ice picture of the Ce-based compounds. The work extends the fermionic-parton classification of DO pyrochlore QSLs beyond the
U(1) sector, where
Z2 topological order is realized equally naturally by fermionic and bosonic spinons.
Abstract We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral U ( 1 ) and Z 2 spin-liquid Ansätze , we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent U ( 1 ) gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.
We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric Z 2 and U ( 1 ) QSLs on the trillium lattice. We find two Z 2 spin-liquids, and a single U ( 1 ) spin-liquid that is proximate to one of the Z 2 states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two Z 2 QSLs is nodal, while the U ( 1 ) case hosts a spinon Fermi surface. One of our Z 2 spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.
We study the uniform
U(1) quantum spin liquid (QSL) with low-energy fermionic quasiparticles for pyrochlore magnets with dipolar-octupolar symmetry, employing a fermionic parton mean-field theory approach. Self-consistent calculations stabilize 12 fully symmetric uniform
U(1) QSLs, of which four mean-field states are ``monopole-flux'' states. Several of these mean-field states show a linear temperature dependence of specific heat at low temperatures, the other phases show a power-law temperature dependence of specific heat $C\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$. The linear temperature dependence of specific heat at low temperatures is reminiscent of the observations in
Nd2ScNbO7. We further compute the dynamic spin structure factors and discuss the possible signature of these fermionic spinons in neutron-scattering experiments.
The diamond lattice has been a promising playground for both classical and quantum spin liquids. Here, the authors conduct a comprehensive symmetry classification of
S=\textonehalf{} quantum spin liquids with SU(2), U(1), and \ensuremath{\mathbb{Z}}
2 gauge fields, and present dynamical spin structure factors within a self-consistent simulation. The authors highlight three discoveries: spinon Ans\"atze with robust gapless nodal loops, topological bands realizing topological insulators, and that Gutzwiller projection of the 0- and $\ensuremath{\pi}$-flux SU(2) spin liquids generates long-range N\'eel order.
We present a general review of the projective symmetry group classification of fermionic quantum spin liquids for lattice models of spin
S=1/2. We then introduce a systematic generalization of the approach for symmetric
Z2 quantum spin liquids to the one of chiral phases (i.e., singlet states that break time reversal and lattice reflection, but conserve their product). We apply this framework to classify and discuss possible chiral spin liquids on triangular and kagome lattices. We give a detailed prescription on how to construct quadratic spinon Hamiltonians and microscopic wave functions for each representation class on these lattices. Among the chiral
Z2 states, we study the subset of U(1) phases variationally in the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{d}$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.