Pre-logarithmic and logarithmic fields in a sandpile model

We consider the unoriented two-dimensional Abelian sandpile model on the half-plane with open and closed boundary conditions, and relate it to the boundary logarithmic conformal field theory with central charge c=-2. Building on previous results, we first perform a complementary lattice analysis of the operator effecting the change of boundary condition between open and closed, which confirms that this operator is a weight -1/8 boundary primary field, whose fusion agrees with lattice calculations. We then consider the operators corresponding to the unit height variable and to a mass insertion at an isolated site of the upper half plane and compute their one-point functions in presence of a boundary containing the two kinds of boundary conditions. We show that the scaling limit of the mass insertion operator is a weight zero logarithmic field.Comment: 18 pages, 9 figures. v2: minor corrections + added appendi

Boundary conditions and defect lines in the Abelian sandpile model

We add a defect line of dissipation, or crack, to the Abelian sandpile model. We find that the defect line renormalizes to separate the two-dimensional plane into two half planes with open boundary conditions. We also show that varying the amount of dissipation at a boundary of the Abelian sandpile model does not affect the universality class of the boundary condition. We demonstrate that a universal coefficient associated with height probabilities near the defect can be used to classify boundary conditions.Comment: 8 pages, 1 figure; suggestions from referees incorporated; to be published in Phys. Rev.

Three-leg correlations in the two component spanning tree on the upper half-plane

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.Comment: 16 pages, 5 figure

Logarithmic two-point correlators in the Abelian sandpile model

We present the detailed calculations of the asymptotics of two-site correlation functions for height variables in the two-dimensional Abelian sandpile model. By using combinatorial methods for the enumeration of spanning trees, we extend the well-known result for the correlation $\sigma_{1,1} \simeq 1/r^4$ of minimal heights $h_1=h_2=1$ to $\sigma_{1,h} = P_{1,h}-P_1P_h$ for height values $h=2,3,4$. These results confirm the dominant logarithmic behaviour $\sigma_{1,h} \simeq (c_h\log r + d_h)/r^4 + {\cal O}(r^{-5})$ for large $r$, predicted by logarithmic conformal field theory based on field identifications obtained previously. We obtain, from our lattice calculations, the explicit values for the coefficients $c_h$ and $d_h$ (the latter are new).Comment: 28 page

Refined conformal spectra in the dimer model

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.Comment: 44 page

Height variables in the Abelian sandpile model: scaling fields and correlations

We compute the lattice 1-site probabilities, on the upper half-plane, of the four height variables in the two-dimensional Abelian sandpile model. We find their exact scaling form when the insertion point is far from the boundary, and when the boundary is either open or closed. Comparing with the predictions of a logarithmic conformal theory with central charge c=-2, we find a full compatibility with the following field assignments: the heights 2, 3 and 4 behave like (an unusual realization of) the logarithmic partner of a primary field with scaling dimension 2, the primary field itself being associated with the height 1 variable. Finite size corrections are also computed and successfully compared with numerical simulations. Relying on these field assignments, we formulate a conjecture for the scaling form of the lattice 2-point correlations of the height variables on the plane, which remain as yet unknown. The way conformal invariance is realized in this system points to a local field theory with c=-2 which is different from the triplet theory.Comment: 68 pages, 17 figures; v2: published version (minor corrections, one comment added

Abelian Sandpile Model on the Honeycomb Lattice

We check the universality properties of the two-dimensional Abelian sandpile model by computing some of its properties on the honeycomb lattice. Exact expressions for unit height correlation functions in presence of boundaries and for different boundary conditions are derived. Also, we study the statistics of the boundaries of avalanche waves by using the theory of SLE and suggest that these curves are conformally invariant and described by SLE2.Comment: 24 pages, 5 figure

Charge ordering in the spinels AlV2_2O4_4 and LiV2_2O4_4

We develop a microscopic theory for the charge ordering (CO) transitions in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$ (under pressure). The high degeneracy of CO states is lifted by a coupling to the rhombohedral lattice deformations which favors transition to a CO state with inequivalent V(1) and V(2) sites forming Kagom\'e and trigonal planes respectively. We construct an extended Hubbard type model including a deformation potential which is treated in unrestricted Hartree Fock approximation and describes correctly the observed first-order CO transition. We also discuss the influence of associated orbital order. Furthermore we suggest that due to different band fillings AlV$_2$O$_4$ should remain metallic while LiV$_2$O$_4$ under pressure should become a semiconductor when charge disproportionation sets in

Topological Surface States and Dirac point tuning in ternary Bi2Te2Se class of topological insulators

Using angle-resolved photoemission spectroscopy, we report electronic structure for representative members of ternary topological insulators. We show that several members of this family, such as Bi2Se2Te, Bi2Te2Se, and GeBi2Te4, exhibit a singly degenerate Dirac-like surface state, while Bi2Se2S is a fully gapped insulator with no measurable surface state. One of these compounds, Bi2Se2Te, shows tunable surface state dispersion upon its electronic alloying with Sb (SbxBi2-xSe2Te series). Other members of the ternary family such as GeBi2Te4 and BiTe1.5S1.5 show an in-gap surface Dirac point, the former of which has been predicted to show nonzero weak topological invariants such as (1;111); thus belonging to a different topological class than BiTe1.5S1.5. The measured band structure presented here will be a valuable guide for interpreting transport, thermoelectric, and thermopower measurements on these compounds. The unique surface band topology observed in these compounds contributes towards identifying designer materials with desired flexibility needed for thermoelectric and spintronic device fabrication.Comment: 9 pages, 6 figures; Related results at http://online.kitp.ucsb.edu/online/topomat11/hasan

CMS endcap RPC gas gap production for upgrade

The CMS experiment will install a RE4 layer of 144 new Resistive Plate Chambers (RPCs) on the existing york YE3 at both endcap regions to trigger high momentum muons from the proton-proton interaction. In this paper, we present the detailed procedures used in the production of new RPC gas gaps adopted in the CMS upgrade. Quality assurance is enforced as ways to maintain the same quality of RPC gas gaps as the existing 432 endcap RPC chambers that have been operational since the beginning of the LHC operation