Effective Hamiltonians and dilution effects in kagome and related antiferromagnets

What is the zero-temperature ordering pattern of a Heisenberg antiferromagnet with large spin length $S$ (and possibly small dilution), on the kagome lattice, or others built from corner-sharing triangles and tetrahedra? First, I summarize the uses of effective Hamiltonians to resolve the large ground-state degeneracy, leading to long-range order of the usual kind. Secondly, I discuss the effects of dilution, in particular to {\it non}-frustration of classical ground states, in that every simplex of spins is optimally satisfied. Of three explanations for this, the most complete is Moessner-Chalker constraint-counting. Quantum zero-point energy may compete with classical exchange energy in a diluted system, creating frustration and enabling a spin-glass state. I suggest that the regime of over 97% occupation is qualitatively different from the more strongly diluted regime.Comment: 11 pages; invited talk at "HFM 2000" (Waterloo, June 2000); submitted to Can. J. Phy

Many-Body Density Matrices for Free Fermions

Building upon an analytical technique introduced by Chung and Peschel [M. Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the density matrix rho_B of a finite block of B sites within an infinite system of free spinless fermions. In terms of the block Green function matrix G (whose elements are G_ij = , where c_i^+ and c_j are fermion creation and annihilation operators acting on sites i and j within the block respectively), the density matrix can be written as rho_B = det(1 - G) exp[ sum_ij (log G(1 - G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.Comment: 12 pages in RevTeX4 format. Uses amsmath, bbold, dcolumn and mathrsfs package

Possible mechanisms for initiating macroscopic left-right asymmetry in developing organisms

How might systematic left-right (L/R) asymmetry of the body plan originate in multicellular animals (and plants)? Somehow, the microscopic handedness of biological molecules must be brought up to macroscopic scales. Basic symmetry principles suggest that the usual "biological" mechanisms -- diffusion and gene regulation -- are insufficient to implement the "right-hand rule" defining a third body axis from the other two. Instead, on the cellular level, "physical" mechanisms (forces and collective dynamic states) are needed involving the long stiff fibers of the cytoskeleton. I discuss some possible scenarios; only in the case of vertebrate internal organs is the answer currently known (and even that is in dispute).Comment: 9 pp latex, 6 figures. Proc. Landau 100 Memorial Conf. (Chernogolovka, June 2008); to appear AIP Conf. series. (v2: added 4 ref's + revised Sec 2.2.