Quantum Phase Transitions of Correlated Electrons and Atoms

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TECHNICAL SUMMARY: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.