Quantum Critical Phenomena and Non Fermi Liquid Physics

Columbia University, New York NY

Investigators

Abstract

TECHNICAL SUMMARY This award supports theoretical research and education to elucidate the principles governing the behavior of materials exhibiting novel electronic orders such as forms of superconductivity and magnetism, to develop the methods needed to reliably calculate these properties, and to apply the knowledge to design and control materials with desired properties. A focus of the research is to further develop and more widely apply new computational methods which have been recently introduced. These "continuous time quantum Monte Carlo" methods have opened up wide classes of previously intractable problems to quantitative investigation. The PI will further improve the methods and use them to gain understanding of the properties of high temperature superconductors and other materials with properties that are beyond those of the standard Landau-Fermi liquid concept. Another theme of the research concerns the properties of materials driven out of equilibrium by a current, voltage, or high intensity optical excitation. Developing a general theory of the nonequilibrium domain raises fundamental intellectual challenges, is essential for understanding the properties of nanoscale devices and has impact on solar energy generation. The PI also aims to advance understanding of quantum criticality. Materials near a quantum critical point typically exhibit large amplitude, long range, slowly changing fluctuations, leading to large deviations from the predictions of Landau-Fermi liquid theory. This project will contribute to the training of young scientists who can look at problems from a broad perspective, combining fundamental insights with concrete applications. The PI is active in organizing and lecturing at summer schools where the ideas generated in condensed matter theory are brought to a wider range of scientists. NONTECHNICAL SUMMARY This award supports theoretical research and education to illuminate fundamental questions such as: How do electrons and atoms, the simple constituents which make up the world around us, combine to produce the astounding variety of behavior found in natural materials? How do we understand these phenomena and control them to produce new kinds of devices and new technologies? The PI will further develop new advanced computational tools and use them to study models of high temperature superconductor materials that exhibit unusual electronic properties in the metallic state that give way to exotic forms of superconductivity as the temperature is lowered. The metallic state of these materials does not conform to the standard model for electrons in metals at low temperatures. In a superconducting state, electrons organize themselves in such way that they can conduct electricity without dissipation. Like the metallic state, superconductivity in high temperature superconductors is also unusual. The PI will explore whether close proximity to a quantum phase transition which occurs at the absolute zero of temperature might be responsible for the unusual features of high temperature superconductors. A quantum phase transition involves the transformation from one state of matter to another driven by the quantum mechanical fluctuations of Heisenberg's uncertainty principle, as opposed to thermal fluctuations which drive more familiar phase transformations like water to steam. The PI will also advance our understanding of systems of many interacting particles that are driven far from the balance of equilibrium, as might occur from a voltage applied to the electrons in small structure of atoms or molecules. The research may have impact across disciplines, including the fields of condensed matter physics, materials science, and electrical engineering. It contributes to the foundations of possible new device technologies at the nanoscale - the scale of atoms and molecules. This project also contributes to the training of young scientists to enable them to combine fundamental insights with concrete applications. The PI is active in organizing and lecturing at summer schools where the ideas generated in condensed matter theory are brought to a wider range of scientists.