a) Γ K M (b) FIG. 1. (Color online) (a) Honeycomb lattice with the different spin exchange interactions considered in this paper; (b) corresponding Brillouin zone with relevant k points. 2 2.5 Velocity [arb. units] J 3 =0 J 3 =0.3

NMR and magnetization measurements in Li2VOSiO4 and Li2VOGeO4 are reported. The analysis of the susceptibility shows that both compounds are two-dimensional S = 1/2 Heisenberg antiferromagnets on a square lattice with a sizable frustration induced by the competition between the superexchange couplings J1 along the sides of the square and J2 along the diagonal. Li2VOSiO4 undergoes a low-temperature phase transition to a collinear order, as theoretically predicted for J2/J1>0.5. Just above the magnetic transition the degeneracy between the two collinear ground states is lifted by the onset of a structural distortion.

11 pages, 17 figuresInternational audienceUsing both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-dimer correlation functions, dimer structure factors and plaquette-plaquette correlation functions provides striking evidence for the presence of a plaquette valence bond solid order in part of the magnetically disordered region

Exact diagonalizations of the spin-1/2 Heisenberg model on the checkerboard lattice have been performed for sizes up to N = 36 in the full Hilbert space and N = 40 in the restricted subspace of first neighbor dimers. This antiferromagnet does not break SU(2) symmetry and displays long range order in 4-spin S=0 plaquettes. Both the symmetry properties of the spectrum and various correlations functions are extensively studied. At variance with the kagomé antiferromagnet, the Heisenberg quantum model on a checkerboard lattice is a Valence Bond Crystal. Some results concerning the 3-dimensional spin-1/2 pyrochlore magnet (for sizes 16 and 32) are also shown: this system could behave differently from its 2-dimensional analog.

Abstract. Extensive calculations in the short-range RVB (Resonating valence bond) subspace on both the trimerized and the regular (non-trimerized) Heisenberg model on the kagomé lattice show that short-range dimer singlets capture the specific low-energy features of both models. In the trimerized case the singlet spectrum splits into bands in which the average number of dimers lying on one type of bonds is fixed. These results are in good agreement with the mean field solution of an effective model recently introduced. For the regular model one gets a continuous, gapless spectrum, in qualitative agreement with exact diagonalization results.

The low-energy singlet dynamics of the Quantum Heisenberg Antiferromagnet on the Kagome lattice is described by a quantitative Quantum Dimer Model. Using advanced numerical tools, the latter is shown to exhibit Valence Bond Crystal order with a large 36-site unit cell and hidden degeneracy between even and odd parities. Evidences are given that this groundstate lies in the vicinity of a Z2 dimer liquid region separated by a Quantum Critical Point. Implications regarding numerical analysis and experiments are discussed. PACS numbers: 74.20.Mn, 67.80.kb, 75.10.Jm, 74.75.Dw, 74.20.Rp The Kagome lattice, a two-dimensional corner-sharing array of triangles shown on Fig. 1(a), is believed to be one of the most frustrated lattices leading to finite entropy in the groundstate (GS) of the classical Heisenberg model [1]. Hence, the Quantum S=1/2 Heisenberg Antiferromagnet (QHAF) on the Kagome lattice is often considered as the paradigm of quantum frustrated magnetism [2] where, in contrast to conventional broken symmetry phases of spin systems (as e.g. magnetic phases), exotic quantum liquids or crystals could be realized. Among the latter, the algebraic (gapless) spin liquid is one of the most intriguing candidate [3].The herbertsmithite [4] compound is one of the few experimental realizations of the S=1/2 Kagome QHAF. The absence of magnetic ordering [5] down to temperatures much smaller than the typical energy scale of the exchange coupling J suggests that, indeed, intrinsic properties of the Kagome QHAF can be observed, even-though Nuclear Magnetic Resonance and Electron Spin Resonance reveal a small fraction of non-magnetic impurities [6] and small Dzyaloshinsky-Moriya anisotropy [7]. So far, the nature of the non-magnetic phase is unknown and confrontation to new theoretical ideas have become necessary. Alternatively, ultra-cold atoms loaded on an optical lattice with tunable interactions might enable to also explore the physics of extended Kagome QHAF [8].The QHAF on the Kagome lattice has been addressed theoretically by Lanczos Exact Diagonalization (LED) of small clusters [9,10]. Despite the fact that the accessible cluster sizes remain very small, these data are consistent with a finite spin gap and an exponential number of singlets within the gap, in agreement with a recent Density Matrix Renormalization Group study [11]. In addition, an analysis of the fourspin correlations pointed towards a short-range dimer liquid phase [12]. Alternatively, a large-N approach [13] and various mappings to low-energy effective Hamiltonians within the singlet subspace [14][15][16] have suggested the formation of translation-symmetry breaking Valence Bond Crystals (VBC). Recently, recent series expansions around the dimer limit [17] showed that a 36-site VBC unit cell is preferred (see Fig 1(a)). In this context, the interpretation of the LED low-energy singlet spectrum remains problematic [18].In this Letter, we use a quantitative dimer-projected effec-E C B A D 108 sites 48 sites (b) (a) 108 sites 36 sites FIG. 1: (color onl...

We consider the effects of doping the Sϭ1/2 kagome lattice with static impurities. We demonstrate that impurities lower the number of low-lying singlet states, induce dimer-dimer correlations of considerable spatial extent, and do not generate free spin degrees of freedom. Most importantly, they experience a highly unconventional mutual repulsion as a direct consequence of the strong spin frustration. These properties are illustrated by exact diagonalization, and are reproduced to semiquantitative accuracy within a dimer resonatingvalence-bond description which affords access to longer length scales. We calculate the local magnetization induced by doped impurities, and consider its implications for nuclear magnetic resonance measurements on known kagome systems.

We introduce for SU(2) quantum spin systems the Valence Bond Entanglement Entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with Quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a Valence Bond Solid state and multiplicative logarithmic corrections for the Neel phase.Comment: 4 pages, 3 figures, v2: small corrections, published versio