Spin-S bilayer Heisenberg models: Mean-field arguments and numerical calculations

Spin-S bilayer Heisenberg models (nearest-neighbor square lattice antiferromagnets in each layer, with antiferromagnetic interlayer couplings) are treated using dimer mean-field theory for general S and high-order expansions about the dimer limit for S=1, 3/2,...,4. We suggest that the transition between the dimer phase at weak intraplane coupling and the Neel phase at strong intraplane coupling is continuous for all S, contrary to a recent suggestion based on Schwinger boson mean-field theory. We also present results for S=1 layers based on expansions about the Ising limit: In every respect the S=1 bilayers appear to behave like S=1/2 bilayers, further supporting our picture for the nature of the order-disorder phase transition.Comment: 6 pages, Revtex 3.0, 8 figures (not embedded in text

Absence of ZAP-70 prevents signaling through the antigen receptor on peripheral blood T cells but not on thymocytes.

Recently, a severe combined immunodeficiency syndrome with a deficiency of CD8+ peripheral T cells and a TCR signal transduction defect in peripheral CD4+ T cells was associated with mutations in ZAP-70. Since TCR signaling is required in developmental decisions resulting in mature CD4 (and CD8) T cells, the presence of peripheral CD4+ T cells expressing TCRs incapable of signaling in these patients is paradoxical. Here, we show that the TCRs on thymocytes, but not peripheral T cells, from a ZAP-70-deficient patient are capable of signaling. Moreover, the TCR on a thymocyte line derived from this patient can signal, and the homologous kinase Syk is present at high levels and is tyrosine phosphorylated after TCR stimulation. Thus, Syk may compensate for the loss of ZAP-70 and account for the thymic selection of at least a subset of T cells (CD4+) in ZAP-70-deficient patients

Convergent expansions for properties of the Heisenberg model for CaV4_4O9_9

We have carried out a wide range of calculations for the $S=1/2$ Heisenberg model with nearest- and second-neighbor interactions on a two-dimensional lattice which describes the geometry of the vanadium ions in the spin-gap system CaV$_4$O$_9$. The methods used were convergent high-order perturbation expansions (``Ising'' and ``Plaquette'' expansions at $T=0$, as well as high-temperature expansions) for quantities such as the uniform susceptibility, sublattice magnetization, and triplet elementary excitation spectrum. Comparison with the data for CaV$_4$O$_9$ indicates that its magnetic properties are well described by nearest-neighbor exchange of about 200K in conjunction with second-neighbor exchange of about 100K.Comment: Uses REVTEX macros. Four pages in two-column format, five postscript figures. Files packaged using uufile

Various series expansions for the bilayer S=1/2 Heisenberg antiferromagnet

Various series expansions have been developed for the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. High temperature expansions are used to calculate the temperature dependence of the susceptibility and specific heat. At T=0, Ising expansions are used to study the properties of the N\'{e}el-ordered phase, while dimer expansions are used to calculate the ground-state properties and excitation spectra of the magnetically disordered phase. The antiferromagnetic order-disorder transition point is determined to be $(J_2/J_1)_c=2.537(5)$. Quantities computed include the staggered magnetization, the susceptibility, the triplet spin-wave excitation spectra, the spin-wave velocity, and the spin-wave stiffness. We also estimates that the ratio of the intra- and inter-layer exchange constants to be $J_2/J_1\simeq 0.07$ for cuprate superconductor $YBa_2Cu_3O_{6.2}$.Comment: RevTeX, 9 figure

Ground State and Elementary Excitations of the S=1 Kagome Heisenberg Antiferromagnet

Low energy spectrum of the S=1 kagom\'e Heisenberg antiferromagnet (KHAF) is studied by means of exact diagonalization and the cluster expansion. The magnitude of the energy gap of the magnetic excitation is consistent with the recent experimental observation for \mpynn. In contrast to the $S=1/2$ KHAF, the non-magnetic excitations have finite energy gap comparable to the magnetic excitation. As a physical picture of the ground state, the hexagon singlet solid state is proposed and verified by variational analysis.Comment: 5 pages, 7 eps figures, 2 tables, Fig. 4 correcte

Tree-level scattering amplitudes from the amplituhedron

7 pages, 2 figures, to be published in the Journal of Physics: Conference Series. Proceedings for the "7th Young Researcher Meeting", Torino, 2016A central problem in quantum field theory is the computation of scattering amplitudes. However, traditional methods are impractical to calculate high order phenomenologically relevant observables. Building on a few decades of astonishing progress in developing non-standard computational techniques, it has been recently conjectured that amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. After providing an introduction to the subject at tree-level, we discuss a special class of differential equations obeyed by the corresponding volume forms. In particular, we show how they fix completely the amplituhedron volume for next-to-maximally helicity violating scattering amplitudes.Peer reviewe

Quantum Sturm-Liouville Equation, Quantum Resolvent, Quantum Integrals, and Quantum KdV : the Fast Decrease Case

We construct quantum operators solving the quantum versions of the Sturm-Liouville equation and the resolvent equation, and show the existence of conserved currents. The construction depends on the following input data: the basic quantum field $O(k)$ and the regularization .Comment: minor correction

Meta-Plaquette Expansion for the Triplet Excitation Spectrum in CaV4_4O9_9

We study antiferromagnetic, $S=1/2$ Heisenberg models with nearest and second neighbor interactions on the one-fifth depleted square lattice which describes the spin degrees of freedom in the spin-gap system CaV$_4$O$_9$. The meta-plaquette expansion for the triplet excitation spectrum is extended to fifth order, and the results are compared with experimental data on CaV$_4$O$_9$. We attempt to locate the phase boundary between magnetically ordered and gapped phases.Comment: 4 figure

Coupling Poisson and Jacobi structures on foliated manifolds

Let M be a differentiable manifold endowed with a foliation F. A Poisson structure P on M is F-coupling if the image of the annihilator of TF by the sharp-morphism defined by P is a normal bundle of the foliation F. This notion extends Sternberg's coupling symplectic form of a particle in a Yang-Mills field. In the present paper we extend Vorobiev's theory of coupling Poisson structures from fiber bundles to foliations and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. Then we discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.Comment: LateX, 38 page