Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.

In this paper we describe the electrons of the non-perturbative one-dimensional (1D) Hubbard model by a fluid of unpaired rotated electrons and a fluid of zero-spin rotated-electron pairs. The rotated electrons are related to the original electrons by a mere unitary transformation. For all finite values of energy and for the whole parameter space of the model this two-fluid picture leads to a description of the energy eigenstates in terms of occupancy configurations of η-spin 1/2 holons, spin 1/2 spinons, and c pseudoparticles only. The electronic degrees of freedom couple to external charge (and spin) probes through the holons and c pseudoparticles (and spinons). Our results refer to very large values of the number of lattice sites Na. The holon (and spinon) charge (and spin) transport is made by 2ν-holon (and 2ν-spinon) composite pseudoparticles such that ν = 1, 2, .... For electronic numbers obeying the inequalities N ≤ Na and N ↓ ≤ N ↑ there are no zero-spin rotated-electron pairs in the ground state and the unpaired-rotated-electron fluid is described by a charge c pseudoparticle fluid and a spin ν = 1 two-spinon pseudoparticle fluid. The spin two-spinon pseudoparticle fluid is the 1D realization of the two-dimensional resonating valence bond spin fluid.

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Ice states, in which frustrated interactions lead to a macroscopic ground-state degeneracy, occur in water ice, in problems of frustrated charge order on the pyrochlore lattice, and in the family of rare-earth magnets collectively known as spin ice. Of particular interest at the moment are "quantum spin-ice" materials, where large quantum fluctuations may permit tunnelling between a macroscopic number of different classical ground states. Here we use zero-temperature quantum Monte Carlo simulations to show how such tunnelling can lift the degeneracy of a spin or charge ice, stabilizing a unique "quantum-ice" ground state-a quantum liquid with excitations described by the Maxwell action of (3+1)-dimensional quantum electrodynamics. We further identify a competing ordered squiggle state, and show how both squiggle and quantum-ice states might be distinguished in neutron scattering experiments on a spin-ice material.

The main characteristic of Mott insulators, as compared to band insulators, is to host low-energy spin fluctuations. In addition, Mott insulators often possess orbital degrees of freedom when crystal-field levels are partially filled. While in the majority of Mott insulators, spins and orbitals develop long-range order, the possibility for the ground state to be a quantum liquid opens new perspectives. In this paper, we provide clear evidence that the spin-orbital SUð4Þ symmetric Kugel-Khomskii model of Mott insulators on the honeycomb lattice is a quantum spin-orbital liquid. The absence of any form of symmetry breakinglattice or SUðNÞ-is supported by a combination of semiclassical and numerical approaches: flavor-wave theory, tensor network algorithm, and exact diagonalizations. In addition, all properties revealed by these methods are very accurately accounted for by a projected variational wave function based on the -flux state of fermions on the honeycomb lattice at 1=4 filling. In that state, correlations are algebraic because of the presence of a Dirac point at the Fermi level, suggesting that the symmetric Kugel-Khomskii model on the honeycomb lattice is an algebraic quantum spin-orbital liquid. This model provides an interesting starting point to understanding the recently discovered spin-orbital-liquid behavior of Ba 3 CuSb 2 O 9 . The present results also suggest the choice of optical lattices with honeycomb geometry in the search for quantum liquids in ultracold four-color fermionic atoms.

Below Eq. (2) in Ref. [1], there is a misprint in the formula relating the scalar product of spin and quadrupolar operators to the permutation operator. The sign in front of the permutation is wrong, and the correct formula readsAs it is written in the Letter, Eq. (5) is valid for pure quadrupolar states (real d 0 s), but not for the general case of complex d 0 s. The correct form of Eq. (5) for the general case readsThis does not affect any of the results reported in the Letter. We have only used this equation to discuss the relationship between the sign of the biquadratic coupling and the type of quadrupolar order (ferroquadrupolar versus antiferroquadrupolar). The determination of the phase diagram has been performed using a different parametrization.

Abstract. The spin 1/2 Heisenberg model on a square lattice with antiferromagnetic nearest-and next-nearest neighbour interactions (the J 1 -J 2 model) has long been studied as a paradigm of a two-dimensional frustrated quantum magnet. Only very recently, however, have the first experimental realisations of such systems been synthesized. The newest material, Pb 2 VO(PO 4 ) 2 seems to have mixed ferro-and antiferromagnetic exchange couplings. In the light of this, we extend the semiclassical treatment of the J 1 -J 2 model to include ferromagnetic interactions, and present an analysis of the finite temperature properties of the model based on the exact diagonalization of 8, 16 and 20 site clusters. We propose that diffuse neutron scattering can be used to resolve the ambiguity inherent in determining the ratio and sign of J 1 and J 2 from thermodynamic properties alone, and use a finite temperature Lanczos algorithm to make predictions for the relevant high temperature spin-spin correlation functions. The possibility of a spin-liquid phase occurring for ferromagnetic J 1 is also briefly discussed.PACS. 71.27.+a Strongly correlated electron systems; heavy fermions -71.10.-w Theory and models of manyelectron systems -75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)

SrCu 2 (BO 3 ) 2 is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as an excellent realization of the Shastry-Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya interactions. Here we demonstrate that these anisotropies, in fact, give rise to topological character in the triplon band structure. The triplons form a new kind of Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps resulting in topological bands with Chern numbers ±2. SrCu 2 (BO 3 ) 2 thus provides a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a threshold value of the magnetic field set by the Dzyaloshinskii-Moriya interactions, the three triplon bands touch once again in a spin-1 Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.