Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions

The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. It is explained why the variational wave-function built by the previous authors is of no help to prove the theorem in dimension larger than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson, Read and Chakraborty gives a strong support to the assertion that the theorem is indeed valid in any dimension. Some illustrations of the general ideas are displayed on exact spectra.Comment: 12 pages, LaTeX with 4 EPS figures embedded in the documen

Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters

Valence bond entanglement entropy of frustrated spin chains

We extend the definition of the recently introduced valence bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1-J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a "good" bipartition should be chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio

When LEP and Tevatron combined with WMAP and XENON100 shed light on the nature of Dark Matter

Recently, several astrophysical data or would-be signals has been observed in different dark-matter oriented experiments. In each case, one could fit the data at the price of specific nature of the coupling between the Standard Model (SM) particles and a light Dark Matter candidate: hadrophobic (INTEGRAL, PAMELA) or leptophobic (WMAP Haze, dijet anomalies of CDF, FERMI Galactic Center observation). In this work, we show that when one takes into account the more recent LEP and Tevatron analysis, a light thermal fermionic Dark Matte (\lesssim 10 GeV) that couples to electrons is mainly ruled out if one combines the analysis with WMAP constraints. We also study the special case of scalar dark matter, using a mono-photon events simulation to constrain the coupling of dark matter to electron.Comment: 8 pages, 6 figure

Low energy excitations of the kagome antiferromagnet and the spin gap issue

In this paper we report the latest results of exact diagonalizations of SU(2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagome lattices). We focus on the low lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagome lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given.The evolution of the intra-S channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We emphasize that the very small intra-S channel energy scale observed in exact spectra is a very interesting information to understand the low T dynamics of this model.Comment: 6 pages, 5 figures, revised version with a more extended discussion on the issue of a possible proximity with a quantum critical point, a few more details and references, a modified Fig

Origins of the Isospin Violation of Dark Matter Interactions

Light dark matter (DM) with a large DM-nucleon spin-independent cross section and furthermore proper isospin violation (ISV) $f_n/f_p\approx-0.7$ may provide a way to understand the confusing DM direct detection results. Combing with the stringent astrophysical and collider constraints, we systematically investigate the origin of ISV first via general operator analyses and further via specifying three kinds of (single) mediators: A light $Z'$ from chiral $U(1)_X$, an approximate spectator Higgs doublet (It can explain the $W+jj$ anomaly simultaneously) and color triplets. In addition, although $Z'$ from an exotic $U(1)_X$ mixing with $U(1)_Y$ generating $f_n=0$, we can combine it with the conventional Higgs to achieve proper ISV. As a concrete example, we propose the $U(1)_X$ model where the $U(1)_X$ charged light sneutrino is the inelastic DM, which dominantly annihilates to light dark states such as $Z'$ with sub-GeV mass. This model can address the recent GoGeNT annual modulation consistent with other DM direct detection results and free of exclusions.Comment: References added and English greatly improve

Intrinsic susceptibility and bond defects in the novel 2D frustrated antiferromagnet Ba2_{2}Sn2_{2}ZnCr7p_{7p}Ga10−7p_{10-7p}O22_{22}

We present microscopic and macroscopic magnetic properties of the highly frustrated antiferromagnet Ba$_{2}$Sn$_{2}$ZnCr$_{7p}$Ga$_{10-7p}$O$_{22}$, respectively probed with NMR and SQUID experiments. The $T$-variation of the intrinsic susceptibility of the Cr$^{3+}$ frustrated kagom\'{e} bilayer, $\chi_{kag}$, displays a maximum around 45 K. The dilution of the magnetic lattice has been studied in detail for $0.29 \leq p \leq0.97$. Novel dilution independent defects, likely related with magnetic bond disorder, are evidenced and discussed. We compare our results to SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$. Both bond defects and spin vacancies do not affect the average susceptibility of the kagom\'{e} bilayers.Comment: Published in Phys. Rev. Lett. 92, 217202 (2004). Only minor changes as compared to previous version. 4 pages, 4 figure

Interaction between static holes in a quantum dimer model on the kagome lattice

A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced [Phys. Rev. B 67, 214413 (2003)]. The ground-state energy of this QDM in presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to 7 lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.Comment: 6 pages, 3 figures. IOP style files included. To appear in J. Phys.: Condens. Matter, Proceedings of the HFM2003 conference, Grenobl