Simulations of Early Baryonic Structure Formation with Stream Velocity: I. Halo Abundance

It has been recently shown that the relative velocity between the dark matter and the baryons (vbc) at the time of recombination can affect the structure formation in the early universe (Tseliakhovich & Hirata 2010). We statistically quantify this effect using large cosmological simulations. We use three different high resolution sets of simulations (with separate transfer functions for baryons and dark matter) that vary in box size, particle number, and the value of the relative velocity between dark matter and baryons. We show that the total number density of halos is suppressed by ~ 20% at z = 25 for vbc = 1{\sigma}(vbc), where {\sigma}(vbc) is the variance of the relative velocity, while for vbc = 3.4{\sigma}(vbc) the relative suppression at the same redshift reaches 50%, remaining at or above the 30% level all the way to z = 11. We also find high abundance of "empty halos", i.e., halos that have gas fraction below half of the cosmic mean baryonic fraction fb. Specifically we find that for vbc = 1{\sigma}(vbc) all halos below 10^5M\odot are empty at z \geq 19. The high abundance of empty halos results in significant delay in the formation of gas rich mini-halos and the first galaxies.Comment: 7 pages, 8 figures, accepted to Ap

Competing Valence Bond Crystals in the Kagome Quantum Dimer Model

The singlet dynamics which plays a major role in the physics of the spin-1/2 Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be approximately described by projecting onto the nearest-neighbor valence bond (NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model which originates from the latter NNVB-projected Heisenberg model via a non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact diagonalisation on a 108-site cluster supplemented by a careful symmetry analysis, it is shown that a previously-found 36-site Valence Bond Crystal (VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}" VBC. The exceptionally large degeneracy of the GS multiplets (144 on our 108-site cluster) might reflect the proximity of the Z_2 dimer liquid. Interestingly, these two VBC "emerge" in {\it different topological sectors}. Implications for the interpretation of numerical results on the QHAF are outlined.Comment: 8 pages, 5 figures, 4 tables; Figure 2 and Table II update

Impurity-doped Kagome Antiferromagnet: A Quantum Dimer Model Approach

The doping of quantum Heisenberg antiferromagnets on the kagome lattice by non-magnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing a) the valence bond crystal (VBC), b) the dimer liquid and c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the Kagome lattice to account for spontaneous creation of mobile S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos Exact Diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small size spinon-impurity bound state appears in some region of the the dimer liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the Valence Bond Glass scenario [R.R.P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the Nuclear Magnetic Resonance spectra of the Herbertsmithite compound are outlined.Comment: Extended version. 9 pages, 11 figure

Confinement and deconfinement of spinons in a frustrated spin-1/2 Heisenberg model

In this publication I discuss the phase diagram of a frustrated spin-1/2 Heisenberg model suggested in A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B{\bf 67}, 024422 (2003). The phase diagram contains $(\pi,0)$ and $(\pi,\pi)$ antiferromagnetic phases separated by the Valence Bond Crystal (VBC) state. I argue that the point of the phase diagram with deconfined spinons, predicted in the aforementioned work, is situated in the middle of VBC state, at the point where the dimerization order parameter changes sign.Comment: 13 pages, 5 figures; an important reference and some explanations adde

Extracting ∣Vbc∣|V_{bc}|, mcm_c and mbm_b from Inclusive DD and BB Decays

Using recent results for nonperturbative contributions to the $B$ and $D$ meson inclusive semileptonic widths, a model independent extraction of \vbc, $m_c$ and $m_b$ is made from the experimentally measured $B$ and $D$ lifetimes and semileptonic branching ratios. Constraining the parameters of the HQET at \CO(1/m_Q^2) by the $D$ semileptonic width, \vbc is found to lie in the range .040<\vbc< 0.057. The $c$ and $b$ quark masses are not well constrained due to uncertainty in the relevant scale of $\alpha_s$. These results assume the validity of perturbative QCD at the low scales relevant to semileptonic charm decay. Without making this assumption, somewhat less stringent bounds on $V_{bc}$ from $B$ decay alone may be obtained.Comment: (revised version - contains a more detailed discussion of the uncertainty in our results from the uncertainty in the scale of \alpha_s) 12 pages, 5 figures included, uses harvmac.tex and epsf.tex, UCSD/PTH 93-25, UTPT 93-21, CMU-HEP 93-1

Generalised Shastry-Sutherland Models in three and higher dimensions

We construct Heisenberg anti-ferromagnetic models in arbitrary dimensions that have isotropic valence bond crystals (VBC) as their exact ground states. The d=2 model is the Shastry-Sutherland model. In the 3-d case we show that it is possible to have a lattice structure, analogous to that of SrCu_2(BO_3)_2, where the stronger bonds are associated with shorter bond lengths. A dimer mean field theory becomes exact at d -> infinity and a systematic 1/d expansion can be developed about it. We study the Neel-VBC transition at large d and find that the transition is first order in even but second order in odd dimensions.Comment: Published version; slightly expande

Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach

The highly-frustrated spin-1/2 quantum Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a {\it small} ferromagnetic next-nearest-neighbor exchange coupling $|J_2|>0.09 J_1$ leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL: instead it possesses a non-trivial flux pattern and large dimerization.Comment: 5 pages, 4 figure

Quantum Melting of Valence Bond Crystal Insulators and Novel Supersolid Phase at Commensurate Density

Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence Bond Crystals (VBC) of resonating particle pairs are stabilized. Their melting into superfluid/metallic phases under increasing hopping is investigated at T=0K. More specifically, we identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.Comment: 4 pages, 5 figures; added references, improved content; fitting with PRL forma