Entanglement and Scattering in 1d and 2d

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NON-TECHNICAL SUMMARY: This award supports fundamental theoretical research and education aimed at advancing our grasp of quantum aspects of condensed matter theory at low dimensions through the study of entanglement and dynamics in many-body states. Many of the most interesting many-body physical systems, such as superconductors and superfluids, involve interactions between many particles, which are governed by the rules of quantum mechanics. One of the quintessential elements of quantum mechanics is called entanglement, the phenomenon that parts of a physical system can be correlated, i.e. "know" what goes on in another part of the system in the sense that a measurement on one will determine the outcome of a measurement on the other, even when the two parts become physically separated. Entanglement is well understood when a small number of particles is concerned, and has even been experimentally demonstrated. The role of entanglement in many-body systems is more complicated and subtle, and is currently under intense study. A related very difficult and important challenge is related to understanding the dynamics of many-body systems. Indeed, our main way of investigating physical systems is by examining their behavior under various external probes such as external magnetic and electric field. Understanding the dynamics of such processes can help explain the collective behaviors of their constituents that are responsible for phenomena such as superconductivity and superfluidity. Entanglement and dynamics are naturally intertwined, as entanglement may affect dynamics, and dynamics may reveal entanglement. The present project will concentrate on both of these effects and their relations, from highly theoretical aspects of entanglement in quantum systems, to the development of methods to analyze actual experimental measurements that involve quantum dynamics such as x-ray scattering on superconductors and neutron scattering experiments in magnetic systems. Characterizing entanglement and dynamics and their relations may also have a potential long-term benefit of providing the keys to controlling quantum systems. The project presents an excellent opportunity to train graduate students and introduce them to these cutting-edge physics problems. The research will also be accompanied by public lectures aimed at the promotion of scientific thinking. TECHNICAL SUMMARY: This award supports fundamental theoretical research on aspects of two-dimensional quantum systems. The main areas of research will involve entanglement and dynamics. The first focus topic will be the investigation of the nature of locality in a quantum lattice system through studying the nature of locality in entanglement Hamiltonians. These are effective Hamiltonians that describe the state of only a part of a quantum system. Recent exciting developments show that in a large class of systems described by conformal field theories, entanglement Hamiltonians may be of relatively simple, local, nature. These systems will be explored from a general field theory perspective, with particular emphasis on the special but crucially important case of fermions. Special attention will be given to the development of new, original, and transformative theoretical ideas. In the second part, some of the same methods, especially those dealing with fermionic determinants, will also be utilized to study dynamical problems. In particular, methods will be developed to analyze the dynamical process essential in resonant x-ray scattering. Such experiments have recently grown into a powerful investigative tool for the study of correlated systems, such as high-temperature superconductors. The interpretation of such measurements necessitates a detailed analysis, which may help disentangle some of the possible mechanisms and ingredients leading to high-temperature superconductivity. In parallel, the effect of quantum fluctuations on low-dimensional spin models motivated by frustration phenomena in magnetism will be studied. The project is expected to engage several different scientific communities, ranging from high-energy physics and mathematics to experiment. Organization of public lectures and training of students will be an integral part of the activity.