Novel Phases of Quantum Matter

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TECHNICAL SUMMARYThis award supports theoretical research and education to explore the properties of strongly interacting quantum matter, as realized in a wide variety of transition metal compounds, and in systems of trapped ultra-cold atoms. Special attention will be paid to layered compounds with antiferromagnetism and higher temperature superconductivity: examples are the cuprates, the pnictide compounds, the Bechgaard salts, and rare-earth heavy-fermion compounds. The PI has proposed a common phase diagram which has successfully described the variation in physical properties as a function of temperature, applied magnetic field, and a tuning parameter like electron density or pressure, across these comprehensive series of materials. Central actors in this phase diagram are quantum phase transitions, involving the onset of spin magnetism and other orders, in metals and superconductors. The PI has described the strong-coupling structure of the theory of such transitions in two spatial dimensions, and proposed to develop the theory to produce new experimental tests of our understanding. The theory also allows for more exotic intermediate phases, with subtle types of quantum entanglement or 'topological order;' the PI will study their features while making contact with experimental studies on certain organic insulators. The theories of strong quantum correlations will also be applied to experiments on trapped ultra-cold atoms, and to electron spin physics in graphene. Finally, there are also remarkable connections between the possible phases of strongly interacting quantum matter, and the states of gravitational theories in anti-de Sitter space, through a gauge-gravity duality. The PI will continue his research at this interface area.This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field. NONTECHNICAL SUMMARYThis award supports theoretical research and education with the aim to explore quantum matter. Quantum matter is formed when large numbers of interacting particles are at temperatures low enough so that the concepts of quantum mechanics play a crucial role in determining its distinguishing characteristics. For electrons in solids, the needed 'low' temperatures can be even higher than room temperature. For gases of trapped atoms, ultra-cold temperatures about one billionth of a degree from the absolute zero of temperature are needed. Remarkably, a common set of ideas has found application across this wide range of energy scales. Some of the most interesting phases of quantum matter are associated with the interplay between magnetism and superconductivity. Electrons may be thought of as tiny magnets and magnetism arises from the co-operative arrangement of the magnetic axes of the electrons. Superconductivity is the ability of pairs of electrons to carry electrical current without dissipation. The PI will study how by varying material parameters, it is possible to drive a system of electrons from a magnetic to a superconducting state, across a variety of 'quantum phase transitions.' Such phase transitions are analogous to familiar thermal transitions, like water changing to steam, but are associated here with subtle quantum correlations between the electrons. Concepts from the theory of quantum phase transitions inform our understanding of the measureable properties of quantum matter in the laboratory.The PI will also explore emerging connections between the theory of quantum matter, and seemingly unrelated work on the quantum theory of black hole horizons. These fields share a common interest in how many particles can become 'entangled' with each other quantum mechanically across large distances; their distinct approaches to entanglement have led to mutually beneficial insights.This award also supports education at the graduate and postdoctoral level, as well as outreach to the public and the preparation of the next edition of an authoritative textbook in the field.