Quantum Entanglement and Dynamics in Lattice Systems

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NONTECHNICAL SUMMARYThis award supports fundamental theoretical research and education aimed at advancing our grasp of quantum aspects of condensed matter theory at low dimensions. The major fundamental difficulty in describing and theoretically representing quantum many-body systems is the vast number of parameters required. The number of such parameters increases exponentially with the number of constituents of a system, and thus quickly becomes intractable for numerical computations, even for small quantum systems. Thus, efficient descriptions of quantum systems are of fundamental importance to our understanding of complex systems and of their applications. In this project, the PI will study a new representation for certain quantum systems that is exact and efficient. Another front of the research is the development of models of quantum systems that efficiently describe their dynamics, for example quantum detectors under the influence of measurements and external disturbances. The detailed understanding of such dynamics may find a crucial role in the development of a host of new experimental diagnostic tools, and of platforms for quantum computing.The project will require the use and development of new theoretical tools in the arsenal of theoretical physics of many-body quantum states. Also, in tandem with the research, the project will involve the training of graduate students in cutting-edge methods of theoretical physics, which are vital for a scientific career but also form a core of ideas that often find new uses in industry.TECHNICAL SUMMARYThis award supports theoretical research and education to advance our grasp of quantum aspects of condensed matter theory at low dimensions through the study of entanglement, dynamics, and fluctuations in many-body states. There are three main topics of study:The first topic is a study of the interplay of locality and entanglement and its relation to variational methods like tensor network states. The PI will focus on recently discovered Hamiltonians that exhibit highly entangled ground states and new phase transitions, and unusual dynamical scaling properties.The second topic will deal with a set of quantum nonequilibrium problems, a topic of current interest due to advancement in theory and experiment. Theory lags significantly behind experimental abilities primarily due to the inability to effectively simulate many-body dynamics. Via a numerical framework based on closed hierarchies of equations, the PI will study nonequilibrium current generation, effects of the motion of detectors and sources in a Fermi sea, quantum wakes, and role of the interplay between disorder and measurements.In a third topic, the PI will investigate a new class of boson impurity models that can be mapped into certain photonic cluster states, with particular emphasis on relating these states to ground states of interesting physical disordered systems that may ultimately be amenable to quantum simulation.The methods and approaches employed and developed will allow for a fruitful exchange of ideas between researchers in condensed matter, quantum information, high-energy physics, and in mathematics. Nonequilibrium quantum physics plays a role in a wide swath of applications from fundamental physics understanding to the development of devices. Finally, an essential component of the project is that it will provide opportunities for the training of new researchers, whose development as scientists is a vital goal of the proposed activity.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.