New Paradigms of Quantum Criticality

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NONTECHNICAL SUMMARYThis award supports theoretical research aimed at describing the connection between physical properties of modern quantum materials and the nature of many-particle quantum entanglement. Conventional theories of electron motion in metals and semiconductors usually treat the motion of each electron independently, in an average environment defined by the other electrons. This independent electron picture has been quite successful in many metals and semiconductors. However, in many newly discovered materials, some of significant technological importance, the subtle quantum correlations between the electrons need to be accounted for, even for an understanding of their macroscopic properties. In particular, quantum entanglement leading to “spooky action at a distance” can be present not only between a pair of electrons, but across long distances and involving large numbers of electrons. A class of materials of particular interest in this research are the cuprate high temperature superconductors, all of which are layered materials containing layers with copper and oxygen atoms arranged in a square lattice. There is accumulating experimental evidence for a "quantum critical point" near a mobile electron density where the highest critical temperature for superconductivity is observed. This theoretical research will describe the phase transition in the electron entanglement across this critical point. New methods for describing many particle entanglement have been developed by the PI and others, and also across different fields of physics, including quantum information theory, high energy particle theory, and quantum gravity. These advances will be synthesized in new theoretical frameworks, and subjected to tests by observations on quantum materials. This award will also contribute to the development of the scientific workforce by supporting the training of graduate students and postdoctoral associates in topics at the forefront of theoretical condensed matter physics. Furthermore, the PI will continue to pursue an active program of public lectures, interviews, colloquia, and lectures at schools for advanced graduate students. TECHNICAL SUMMARYThis award supports theoretical research which will examine models of quantum criticality involving gauge theories coupled to finite density matter. While much is known about phase transitions of gauge theories coupled to relativistic matter in 2+1 spacetime dimensions, applications to cuprate criticality require finite density fermionic matter which, in the absence of disorder, has a sharp Fermi surface. The PI and his research team have proposed specific gauge theories for cuprate criticality which satisfy numerous phenomenological constraints imposed by observations. In some mathematical contexts, the combination of the gauge structure and the presence of a Fermi surface leads to effective quantum field theories which are bilocal in time. Currently, little is understood about such bilocal theories in 2+1 dimensions, and unraveling this mystery will be an important focus of this research. Previously, bilocal theories have appeared in models with infinite-range interactions, like the Sachdev-Ye-Kitaev (SYK) models, which have some attractive phenomenological features. Insights gained from the study of SYK models will be applied to the more realistic bilocal field theories appearing in this research. Another focus area of the research will be on the thermal Hall effect: In the most recent experiments, the thermal Hall effect has emerged as a powerful diagnostic probe of quantum phase transitions associated with changes in entanglement structure. The PI and his team will extend theories of the thermal Hall effect to models of the pseudogap phase of the cuprates. In addition, correlated electron superconductivity in twisted graphene bilayers will be studied, with a focus on the quantum interplay of multiple competing orders and superconductivity.This award will also contribute to the development of the scientific workforce by supporting the training of graduate students and postdoctoral associates in topics at the forefront of theoretical condensed matter physics. Furthermore, the PI will continue to pursue an active program of public lectures, interviews, colloquia, and lectures at schools for advanced graduate students.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.