Computational Studies of Entanglement and Thermodynamics of Strongly Interacting Spin Systems

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NONTECHNICAL SUMMARYThis award supports theoretical and computational modeling of novel phases of matter in materials. From magnets to metals to semiconductors and superconductors, the properties of these materials are determined by electrons moving in the intricate crystalline environment of a given material and cooperating with each other due to the principles of quantum mechanics and electrostatic Coulomb interactions. New electronic states can emerge from the correlated motion of electrons. The PI will study phases of electrons in models for materials that can: (i) provide insight into how new phenomena and properties emerge as a result of complex cooperative behavior of a large number of electrons, and (ii) present experimental scientists with possible materials with properties that can be controlled externally in novel ways, allowing for various devices and applications. Examples of electronic phases to be studied include those in high temperature superconductors, systems that are close to transforming from a metal to an insulator, and materials that exhibit unusual forms of magnetism. While focused primarily on the study of phenomena in materials, this project has deep connections with fundamentals of quantum field theory and even geometry, topology and quantum gravity.Educational components of this project involve training graduate and advanced undergraduate students in the areas of Computational Physics, with skills that would be broadly useful over all areas of science and engineering. It would also involve interacting with high school students through the California Summer School for Math and Science program of the University of California, where the PI would develop and teach courses suitable for these students. TECHNICAL SUMMARYThis award supports theoretical and computational modeling of novel electronic phases of matter in materials. Quantum mechanics underlies much of our understanding of solid state physics. This project deals with exotic quantum phases that defy conventional paradigms of many-electron behavior. Strongly competing interactions between electrons and their spins can lead to frustration and exotic quantum phases, where new degrees of freedom can emerge. The PI will focus particularly on the existence of novel quantum phases of matter in real magnetic materials with competing or frustrating exchange interactions. Such phases can support emergent fields and particles inside the materials that are not found elsewhere. The PI will pursue systematic calculations of thermodynamic and spectral properties of appropriate models, with and without quenched disorder using high-temperature series expansions and numerical linked cluster expansions. This will help establish the connection between models and materials. Systems to be studied include quantum spin-ice materials and Kagome-Lattice Heisenberg systems. The PI will work with experimental groups to understand such phenomena as unconventional superconductivity in the iron-pnictide materials, quantum spin-ice behavior and emergent quantum electrodynamics in rare-earth pyrochlores such as ytterbium titanate, and quantum spin-liquids in kagome and triangular lattice antiferromagnets.Another focus of the project is the study of quantum entanglement in many-body systems. Using series expansion methods, the PI will calculate ground state entanglement entropies in various lattice-statistical models. These calculations should be informative about quantum phase transitions and critical phenomena, Fermi-surface geometry and topological phases of matter. In addition, this subject also has deep connections with quantum information theory, quantum field theory, geometry, topology and even quantum gravity.Educational components of the project involve training graduate and undergraduate students in methods of theoretical and computational physics that should be broadly useful in science and industry. In addition the PI will work with talented high school students through the California Summer School for Math and Science program of the University of California and with underrepresented students through the Mentorship for Undergraduate Research Participants in the Physical and Mathematical Sciences program.