This grant supports theoretical research on strongly interacting condensed matter systems. These systems are ones in which electrons in solids are dramatically affected by their strong interactions and their disordered state. The theoretical study of these type of systems requires new theoretical methods. Experimental, and preliminary theoretical, studies have revealed a wealth of new and exotic states of matter. While the research is at the core of modern condensed matter physics, the results may impact our understanding of nanophysics and quantum computation.
Intellectual Merit
With increasing regularity, new and more refined experiments on "novel" electronic materials are revealing - and sharpening - dramatic deviations from the standard paradigm of solid state physics based on Fermi liquid theory. Deviations are especially striking in the d-shell transition metal oxides, the f-shell rare earth compounds as well as some organic molecular crystals. This dire situation points to the need and urgency of developing a new theoretical paradigm for strongly interacting many-fermion systems. Current theoretical advances are being fueled by novel reformulations of 2d and 3d models of interacting electrons involving Z2 and U(1) gauge theories and boson-vortex duality transformations, among others. The existence of a slew of exotic quantum phases and transitions have emerged including, 2d and 3d Mott insulators with topological order, 2d "critical" spin liquid insulators, 2d non-Fermi liquid conductors and novel deconfined quantum criticality. Convergence between theory and experiment has been intermitant, but with increasing promise. Here, the intention is to exploit a new approach to 2d quantum systems which combines gauge theory with Chern-Simons statistics transmutation, to help push this effort forward. Progress should be possible in the following areas: 1. Advancing our understanding of topologically ordered spin liquid insulators, especially the 2d Kagome antiferromagnet, and the possible realization of the 3d U(1) spin liquid on a cubic optical lattice in ultracold atomic systems. 2. Exploring "critical" algebraic spin liquids in 2d, and confronting experiments in the cuprate pseudo-gap and in the organic Mott insulator k(BEDT)2X. 3. Developing a description of 2d Non-Fermi liquid conductors by fermionizing holons and vortices, to address the "strange metals" seen in the cuprates and MoGe supeconducting films. 4. Extending our recent understanding of "deconfined quantum criticality" to include itinerant electron systems, with an eye towards heavy fermion quantum criticality. 5. Generalizing the theoretical analysis of transport through a point contact in a 1d (bosonic) Luttinger liquid, to a Josephson weak link between 2d superconducting films, and confronting existing nano-wire experiments.
Broader Impact
Based on recent successes such as the observation of clear Luttinger liquid physics in carbon nanotubes, it is clear that any theoretical advances in our understanding of complex many-electron systems will help the fledgling nanophysics effort. More specifically, the effort to understand and control exotic quantum phases with topological order will be critical if the proposal to employ such phases to perform "decoherence free" quantum computation will ever be fulfilled.
