Geometrical Approaches to Frustrated and Many-Body Systems

Cornell University, Ithaca NY

Investigators

Abstract

0240953 Henley This award supports theoretical and computational research and education seeking to elucidate the origins and effects of strong correlations in fermion and boson systems and the role of frustration in spin systems. The research has three focus areas. I. A model of spinless fermions with neighbor exclusion will be further studied, via variational wavefunctions for holes moving on the stripes, the charged, quantum fluctuating antiphase boundaries, found in this model and for analytic justification of the low-density fermi liquid. A Wigner-crystal-like phase is a candidate for spontaneous currents, as is a 2 1 ladder. II. A truncation scheme for interacting-fermion Hamiltonians on lattices is aimed at constructing renormalized creation operators on blocks of sites by a sort of canonical transformation, and thereby extracting quasiparticle dispersion relations. It will be tested for the square-lattice, neighbor-excluded spinless fermion model. An alternative truncation criterion for such blocks will be tested, that uses the (many-particle) density matrix on clusters overlapping the blocks, to optimize the translational invariance of the truncated wavefunction. Finally, adaptations of the Cluster Dynamic Mean Field Theory will be explored, that replace single-electron Green's functions on a block by a dynamic version of the block's density matrix, III. Spin correlations will be predicted for the highly frustrated and degenerate pyrochlore lattice antiferromagnets, in two regimes. For the disordered regime, unusual singularities in the diffuse neutron diffraction pattern will be explained in terms of the constraint of zero total spin in each tetrahedron, and a complete ?ting form will be developed. In the large-S Heisenberg spin regime, an effective Hamiltonian of Ising-gauge form will be investigated as encoding the ground-state selection effects of harmonic spin-waves, and the exact ordering pattern will be derived from spin-wave expansion to anharmonic order. In two-dimensional models, a high-?eld square lattice spin model and a similar "quantum 6-vertex model" will be investigated using the map to an interface and coarse-graining, to extract dynamic structure factors. Projects I and II are aimed at the fundamental question: how can we truly understand the groundstate correlations of a strongly interacting model, possibly in an exotic quantum state, when brute-force computational power is inevitably too limited? Rather than augment computational power, the PI seeks to make better use of potential information in any simulation, by understanding better what degrees of freedom are the most important, and what additional quantities are desirable to measure. The style of this research is pertinent to pedagogical goals: the priority is to develop pictures that fairly represent the fundamental reasons for a phenomenon, or counter-examples that force a re-thinking of common assumptions, rather than produce close fits of experimental results. This motivates a search for the simplest concrete model that exhibits a particular effect. Rather than adapting well-known techniques to additional systems for which answers are desired, these projects aim to develop new techniques, that complement existing techniques by providing a different viewpoint and hopefully by being more concrete or transparent (e.g. preferring real over Fourier space or direct mappings over dualities, when either way will work). Project III is motivated by ongoing experiments in highly frustrated magnets. This area has the potential to be a rich source of interesting strongly interacting systems. The complicated lattices and ordering patterns provide much scope for the geometrical approach that has been a theme of the PI's work. Broader impacts of this work include graduate and higher level education in modern condensed matter theory and the possibility that this research creates tools and insights that not only lead to progress on rich and difficult problems of strongly correlated electron systems, but are also applicable to broader areas of condensed matter physics. %%% This award supports theoretical and computational research and education seeking to elucidate the origins and physics of strongly correlated electron materials and the role of frustration in spin systems. The research involves the creative blending of advanced theoretical techniques, computation, and nonstandard models to develop new techniques and physical insights into the rich and exotic quantum mechanical states displayed in strongly correlated electron materials. A thrust of the research aims to maximize information obtained from computational simulations on small systems. Another focus of the research involves systems of spins with geometric arrangements that are not compatible with the interactions between them. Understanding the effects of this frustration observed in some materials may open avenues to the discovery of new materials that may exhibit qualitatively new strongly correlated quantum states. The broader impacts of this work lie in graduate and higher level education in the modern condensed matter theory and in the possibility that this research creates tools and insights that not only lead to progress on a notoriously hard problem but find application outside the original area of research. ***