We propose to study a novel class of quantum phases of matter -- so-called `Fracton' phase of matter, whose quasiparticle excitations, known as sub-dimensional particles, have restricted mobility or kinetic motions. Fracton phases emerge from a rich interplay of correlations, symmetry, topology, and dynamics in strongly interacting many-body systems. These exotic phases extend and challenge our existing notions of topological order and have attracted broad interdisciplinary interest including topological physics, quantum field theory, gravity, quantum information, and elasticity theory. This proposal aims to build an effective field theory framework to classify, characterize, simulate, and detect distinct fracton phases and search for potential application of fracton for quantum memory and quantum computing both at equilibrium and in dynamical processes. We will apply a multidisciplinary approach combining the latest advances in quantum field theory, quantum information, and condensed matter to design new characterization tools to reveal exotic features of fracton dynamics, explore the microscopic realization of fracton physics and seek new experimental fingerprints to probe these phases. Our research will gravitate around the important question of how dynamical constraints and higher-moment conservation law can engender new types of quantum matter or critical points, and how constraint motion of the quasiparticle can engender robust information storage at intermediate time-scales in quantum many-body systems. We expect the research outcome can expand our understanding of new types of quantum phenomena with constraint dynamics, and shed light for investigating how strong interactions can potentially help identify promising platforms for quantum information storage and processing.
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