Longitudinal excitations in quantum antiferromagnets

By extending our recently proposed magnon-density-waves to low dimensions, we investigate, using a microscopic many-body approach, the longitudinal excitations of the quasi-one-dimensional (quasi-1d) and quasi-2d Heisenberg antiferromagnetic systems on a bipartite lattice with a general spin quantum number. We obtain the full energy spectrum of the longitudinal mode as a function of the coupling constants in the original lattice Hamiltonian and find that it always has a non-zero energy gap if the ground state has a long-range order and becomes gapless for the pure isotropic 1d model. The numerical value of the minimum gap in our approximation agrees with that of a longitudinal mode observed in the quasi-1d antiferromagnetic compound KCuF${}_3$ at low temperature. It will be interesting to compare values of the energy spectrum at other momenta if their experimental results are available.Comment: 19 pages, 4 figure

Excited states of quantum many-body interacting systems: A variational coupled-cluster description

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.Comment: 17 pages, 4 figure

On a property of random-oriented percolation in a quadrant

Grimmett's random-orientation percolation is formulated as follows. The square lattice is used to generate an oriented graph such that each edge is oriented rightwards (resp. upwards) with probability $p$ and leftwards (resp. downwards) otherwise. We consider a variation of Grimmett's model proposed by Hegarty, in which edges are oriented away from the origin with probability $p$, and towards it with probability $1-p$, which implies rotational instead of translational symmetry. We show that both models could be considered as special cases of random-oriented percolation in the NE-quadrant, provided that the critical value for the latter is 1/2. As a corollary, we unconditionally obtain a non-trivial lower bound for the critical value of Hegarty's random-orientation model. The second part of the paper is devoted to higher dimensions and we show that the Grimmett model percolates in any slab of height at least 3 in $\mathbb{Z}^3$.Comment: The abstract has been updated, discussion has been added to the end of the articl

Spectroscopic studies of a phosphoinositide-binding peptide from gelsolin: behavior in solutions of mixed solvent and anionic micelles

The peptide G(150–169) corresponds to a phosphatidylinositol 4,5-bisphosphate (PIP2) and filamentous actin (F-actin) binding site on gelsolin (residues 150–169, with the sequence KHVVPNEVVVQRLFQVKGRR). The conformation of this peptide in trifluoroethanol (TFE) aqueous solution was determined by 1H nuclear magnetic resonance as the first step toward understanding the structural aspects of the interaction of G(150–169) and PIP2. The circular dichroism experiments show that G(150–169) adopts a predominantly alpha-helical form in both 50% TFE aqueous solution and in the presence of PIP2 micelles, therefore establishing a connection between the two conformations. 1H nuclear magnetic resonance experiments of G(150–169) in TFE co-solvent show that the helical region extends from Pro-154 to Lys-166. The amphiphilic nature of this helical structure may be the key to understanding the binding of the peptide to lipids. Sodium dodecyl sulfate micelle solution is used as a model for anionic lipid environments. Preliminary studies of the conformation of G(150–169) in sodium dodecyl sulfate micelle solution show that the peptide forms an alpha-helix similar to but with some structural differences from that in TFE co-solvent. Fluorescence experiments provide evidence of peptide clustering over a narrow range of peptide/PIP2 ratios, which is potentially relevant to the biological function of PIP2