This award supports theoretical research and education aiming to understand materials in the vicinity of quantum phase transitions. Quantum phase transitions occur across critical points where there is a qualitative change in the quantum mechanical ground state. By tuning parameters, such as carrier concentration, magnetic field strength, or pressure, new quantum phases with novel physical properties have been discovered. The PI aims to carry out a variety of theoretical studies motivated by remarkable experimental progress in Cu-based transition metal oxides, in organic compounds, in optical lattices of ultracold atoms, and in graphene. These examples include novel insulating spin gap states with evidence for valence bond solid order, one of which becomes a superconductor under applied pressure. The PI will study transitions between such phases which are metals, insulators, or superconductors. Many of these phases are characterized by exotic topological orders. The PI will study the response of such phases to impurities and other local perturbations, to make contact with nanoscale experimental probes such as the scanning tunneling microscope. The PI will also pursue investigations in the `quantum critical' region, found at intermediate temperatures near a quantum critical point, which has applications to observations in the underdoped cuprates, in thin superconducting films and wires, and in graphene. The PI has developed new tools to address quantum criticality by adapting advances in the string theory description of black holes. He plans to expand the reach of such tools to a wider class of strongly interacting many-body systems.
This award supports activities beyond the research thrust, including connections with the global scientific community through visiting post-doctoral fellows, supported by fellowships from their home countries, the preparation of a more accessible second edition of the PI?s book ?Quantum Phase Transitions? which summarizes key ideas behind this research for graduate students.
NON-TECHNICAL SUMMARY: This award supports theoretical research and education that aims to predict new states of matter and understand transformations among them and known states of matter. The research focuses on transformations that occur at the absolute zero of temperature in response to changes in a physical parameter such as pressure or the strength of interaction between electrons. Unlike more familiar transformations, like water to steam, these transformations of phase are not a consequence of changes in temperature. Rather they are a consequence of Heisenberg?s uncertainty principle, a cornerstone of quantum mechanics. These quantum phase transitions may be realized between new states of matter that may exist in high temperature superconductors, a class of organic conductors, systems of cold atoms trapped by light, and more. The PI?s work utilizes advanced theoretical techniques that benefit from ?cross-pollination? with branches of physics that study subatomic particles and the origins of gravity.
This award supports activities beyond the research thrust, including connections with the global scientific community through visiting post-doctoral fellows, supported by fellowships from their home countries, the preparation of a more accessible second edition of the PI?s book ?Quantum Phase Transitions? which summarizes key ideas behind this research for graduate students.
Superconductivity is the ability of certain metals to conduct electricity without appreciable resistance. Such metals are of great practical importance, but also raise fundamental questions on the quantum theory of itinerant electrons in metals. The last three decades have seen the development of many new superconductors, displaying superconductivity at relatively high temperatures. We have developed a unifying theory of these superconductors, and the interplay of superconductivity with their magnetism. Our theory has resulted in the phase diagram shown, and has been found to be in excellent agreements with numerous recent experiments. Underlying our theory of the new superconductors is the theory of quantum phase transitions: these are transitions at absolute zero, driven by fluctuations demanded by Heisenberg's Uncertainty Principle. The P.I. had written a well-reviewed and popular book on this subject. The just released second edition is significantly expanded and contains an in-depth treatment of introductory material, suitable for adoption in a course for graduate students. Many of the key puzzles in the theory of these new materials relate to the complex nature of the "quantum entanglement" in the many-body state. Such entanglement is also present in certain insulators, called spin-liquids, and our research involved a detailed theory and classification of spin liquids. We also developed a framework for describing spin liquids co-existing with metals. We believe this will be crucial for describing an emerging class of electronic materials, including some of the superconductors with the highest critical temperatures. We also developed new theoretical methods for describing quantum many-body states with long-range entanglement, such as those found near quantum phase transitions. One of these involves a surprising connection to string theory. Many string-theorists are now using these methods to describe strongly interacting states of quantum matter from a whole new perspective.
