We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Motivated by recent experiments on the Heisenberg S = 1/2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.PACS numbers: 75.10. Jm, 75.10.Kt, 75.30.Kz, 75.10.Pq When low dimensionality, geometric frustration, and antiferromagnetism conspire in quantum magnets, completely novel and exotic physics can emerge at low temperature. In such quantum spin liquid (QSL) phases, the picture of classical magnetic moments breaks down, and fractionalized spinon quasiparticles with unusual statistics and long-range entanglement properties become relevant [1]. After intense theoretical research activity on quantum spin liquids in the late 1980's and 1990's due to their intimate relation with high-temperature superconductivity [2], interest in QSL has recently regained momentum because of possible applications in quantum computing [3]. More strikingly, however, enormous experimental progress in synthetization and characterization of actual spin liquid candidate materials has catapulted the field to an unprecedented stage of maturity in this century (see and references therein).A highly interesting, recently synthesized QSL candidate material is the so-called kapellasite [14][15][16][17]: X-ray diffraction on powder samples of this strong Mott insulator indicates geometrically perfect, uncoupled twodimensional kagome layers of spin S = 1/2 Cu ions, despite some on-site Cu/Zn dilution. Muon spectroscopy shows the absence of frozen moments, inelastic neutron scattering exhibits a continuum of excitations (mimicking a spinon continuum), and the plateau in 1/T 1 of NMR measurements confirms a fluctuating behavior down to 20 mK. Experiments on kapellasite therefore provide quite strong evidence in favor of a genuine gapless QSL phase in this material.In contrast to its polymorph herbertsmithite [12, 13] -one of the best studied QSL candidate to date -kapellasite is known to have important exchange interactions between farther-neighbor sites in the kagome plane [18,19]. Recent accurate high-temperature series expansions and their fits to susceptibility and specific heat data revealed ferromagnetic interactions on first and second neighbors, while a dominant antiferromagnetic exchange of J d 16 K is present across the hexagons of the lattice [16,17].These results open up exciting new theoretical prospects, because classical spin models on the kagome lattice with such farther-neighbor inte...

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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ states, we study the subset of U(1) phases variationally in the antiferromagnetic $J_1$-$J_2$-$J_d$ Heisenberg model on the kagome lattice. We discuss static spin structure factors and symmetry constraints on the bulk spectra of these phases.Comment: 21+7 pages, 9 figs, 9 tabs; published versio