Geometrical Approaches to Frustrated and/or Diluted Antiferromagnets

Cornell University, Ithaca NY

Investigators

Abstract

This grant supports theoretical research in fundamental condensed matter theory. In particular, four projects relating to geometrical studies of frustrated and diluted antiferromagnets will be investigated. 1. Strongly interacting fermions and reduced density matrices: The correlation density matrix method allows the detection of all possible correlation functions, given a wavefunction from exact diagonalization. It will be tested on systems believed to have rapidly decaying correlations. Renormalization groups (RG) for strongly correlated systems will be revisited, to clarify the relationships or comparisons between (i) contractor renormalization (CoRE); (ii) cluster dynamical mean-field theory; and (iii) the matrix-product ansatz of DM-RG to dimensions d > 1. Also, strong-coupling ladder and d = 2 spinless fermion models will be exhibited on which spontaneous currents develop as a symmetry breaking. 2. Highly frustrated antiferromagnets: An effective Hamiltonian will be derived (by numerical fitting or analytics) from the quartic-order spinwave zero-point energy for the large-S Heisenberg anti-ferromagnet on the pyrochlore lattice. A semiclassical approach will be developed for S = 1, S = 3=2, or S = 2 Heisenberg antiferromagnet on the kagome lattice, based on tunneling between the discrete coplanar states. Magnetization relaxation in spin-ice pyrochlores will be modeled in terms of the coarse-grained polarization and a semiconductor analogy. A long-wavelength theory will be written to describe the helimagnetism in (highly frustrated) spinel CdCr2O4 due (probably) to Dzyaloshinskii-Moriya anisotropy and lattice distortions. 3. Height models and Rokhsar-Kivelson points : A hypothetical antiferromagnet with Ising-like anisotropic exchange in a large field will be mapped to the quantum dimer model, and its spin structure factor calculated. The dimer model will also be studied near the maximum tilt limit in which configurations are mapped to an array of non-crossing, transversely wandering lines. Models will be concocted with topological order, labeled by the simplest discrete groups, and simulated as classical systems. 4. Heisenberg antiferromagnet at percolation: The renormalization group of Chakravarty, Halperin, and Nelson will be translated to the fractal lattice of a critical percolation cluster. Intellectual merit The intellectual focus is on strongly correlated magnetic systems which derive from local geometry causing frustration among spins. These are core issues in modern condensed matter physics. Most of these projects attempt to open up some new tools, not for a grand swath of physics but for particular topics of current interest: tricks for calculating effective Hamiltonians (part 2), models as playgrounds of topological order (part 3), a novel variety of RG (part 4). When it worked, (like our recent gauge-like effective Hamiltonian), I think the results were elementary, elegant, and unexpected; these projects, if successful, would be similar. Broader impacts The grant will contribute to the education and training of students. The primary broader impact is through advances in intellectual merit. Highly frustrated magnets (part 2 of proposal) may well have interesting thermopower properties since they are usually insulators but have large specific heats due to many nearly degenerate states. Also, topological order (part 3) is being energetically pursued in frustrated models with the motivation of quantum computation. Projects 2.3, 2.4, and 4 especially relate to recent neutron-diffraction or magnetic relaxation experiments that are curiosity-driven. In many projects (1.1, 2.2, 3.2, and 4), I hope to get access to the data of computational physicists and to assist their work.