Quantum Critical Phenomena and Non Fermi Liquid Physics

Columbia University, New York NY

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports theoretical and computational research to advance understanding of strongly interacting electrons in equilibrium and in situations far from the steady state of equilibrium. Superconductivity, magnetism, conversion of light into electrical energy: the astonishing variety of behavior found in `electrically active' materials arise from the combination of quantum mechanics and the electrical repulsion between electrons. Understanding this behavior is one of the grand challenges of modern science. Controlling it would create new technologies that can improve all of our lives. However this `many electron' problem is one of the classic hard problems of theoretical science. The research supported by this award builds on exciting recent developments in computers, algorithms and physics concepts, some of them invented by the PI, that are transforming the capability to solve these problems. The PI will further develop, implement and use these new ideas and new computational methods to understand, design, optimize and exploit materials with new kinds of important electronic properties. A central focus of this research is to use the new methods to understand what happens when an electrically active material is challenged by an applied current, electrical impulse, or light wave, because how a material responds to such a challenged determines its technological utility. TECHNICAL SUMMARY This award supports theoretical and computational studies of the physics of strongly interacting electrons in both equilibrium and nonequilibrium situations. A key aspect of the proposed research is the further development and wider application of new classes of computational methods that the PI and other groups have recently introduced. New methods are needed because the combination of quantum mechanical entanglement and electron-electron interactions makes the many-electron problem formally unsolvable for large systems. The difficulties are compounded in the nonequilibrium situation, which is relevant to devices and to new classes of pump-probe experiments, where even the basic theoretical concepts are unclear. The PI will build on discoveries made by many NSF-supported researchers over the years, relating to the use of stochastic methods, such as Monte Carlo, to estimate the value of a Feynman diagram series. These methods have opened up wide classes of previously intractable problems to quantitative investigation. The PI will use them to gain new insights into the superconducting properties of novel materials by constructing and studying in detail the superconducting and pseudogap states of the two dimensional Hubbard model and relating these to the magnetic properties which can now be calculated using the vertex correction methodology developed in the previous funding period. The PI will also explore new applications of the stochastic exploration of diagram series approach to the nonequilibrium case. The straightforward extensions the PI pioneered in previous funding periods do not permit access to physics on long-time scales, but new work based on expansions around analytically determined partial resummations seems to allow access to the long-time limit. The PI will use these methods to develop solvers for the equations of nonequilibrium dynamical mean field theory. In a third research thrust the PI will use analytical methods to examine the interplay of superconducting, antiferromagnetic and `nematic' phases and fluctuations in the iron-pnictide superconductors.