Exotic Quantum Phases and Criticality

该补助金支持强相互作用凝聚态系统的理论研究。 在这些系统中，固体中的电子受到它们强相互作用和无序状态的显著影响。 这类系统的理论研究需要新的理论方法。 实验和初步的理论研究已经揭示了大量新的和奇异的物质状态。 虽然这项研究是现代凝聚态物理学的核心，但其结果可能会影响我们对纳米物理学和量子计算的理解。智力价值随着越来越多的规律性，对“新型”电子材料的新的和更精细的实验正在揭示-并加剧-与基于费米液体理论的固态物理学标准范式的巨大偏差。在d-壳层过渡金属氧化物、f-壳层稀土化合物以及某些有机分子晶体中，偏差尤其显著。这种可怕的情况表明，需要和迫切性，发展一个新的理论范式的强相互作用的多费米子系统。 目前的理论进展正在推动新的2d和3d模型的相互作用电子涉及Z2和U（1）规范理论和玻色子涡旋对偶变换，等等。一系列奇异量子相和跃迁的存在已经出现，包括具有拓扑有序的2d和3d Mott绝缘体，2d“临界”自旋液体绝缘体，2d非费米液体导体和新颖的非限定量子临界性。理论和实验的趋同一直是不确定的，但前景越来越好。在这里，我们的目的是利用一种新的方法来二维量子系统，结合规范理论与陈-西蒙斯统计嬗变，以帮助推动这一努力。在以下领域应该有可能取得进展：1.推进了我们对拓扑有序自旋液体绝缘体，特别是2d Kagome反铁磁体的理解，以及超冷原子系统中3d U（1）自旋液体在双光子晶格上的可能实现.探索“临界”的代数自旋液体在2D，面对实验中的cupratepseudo-gap和在有机莫特绝缘体k（BEDT）2X。通过费米子化和涡旋描述二维非费米液体导体，以解决在铜氧化物和MoGe超导膜中看到的“奇怪金属”。将我们最近对“非限定量子临界性”的理解扩展到包括巡回电子系统，着眼于重费米子量子临界性。将一维（玻色子）Luttinger液体中通过点接触传输的理论分析推广到二维超导膜之间的约瑟夫森弱连接，并面对现有的纳米线实验。更广泛的影响基于最近的成功，如在碳纳米管中观察到清晰的Luttinger液体物理，很明显，我们对复杂的多电子系统的理解的任何理论进展都将有助于新兴的纳米物理学工作。更具体地说，理解和控制具有拓扑有序的奇异量子相位的努力将是至关重要的，如果使用这样的相位来执行“无退相干”量子计算的建议将永远得以实现。

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 MeritWith increasing regularity, new and more refined experiments on "novel" electronic materialsare 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 theoryand 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 cubicoptical lattice in ultracold atomic systems.2. Exploring "critical" algebraic spin liquids in 2d, and confronting experiments in the cupratepseudo-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 itinerantelectron 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 confrontingexisting nano-wire experiments.Broader ImpactBased 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.