Universality and topology in gapless systems and far from equilibrium

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Materials used for electronic devices have many microscopic imperfections, defects, and other sample-to-sample variations. Despite this, at macroscopic scales, the collective properties of many electrons at very low temperatures display striking "universal" behaviors that are remarkably insensitive to these complicated microscopic details. Dramatic examples of universal quantum phenomena include universal scaling laws for how thermodynamic and transport properties depend on control-knobs such as frequency, temperature and field-strength near quantum phase transitions, and topological phases of matter such as quantum Hall fluids and topological insulators that exhibit precisely quantized electrical and thermal transport properties tied to sharply-quantized topological invariants. In the past decade, a remarkable confluence of ideas from solid-state physics, quantum field theory, quantum information theory, and formal mathematics have produced an essentially complete theoretical framework for understanding and characterizing such topological phases in insulating or superconducting (gapped) matter in thermal equilibrium at low-temperature. These theoretical advances have, in turn, driven materials discovery of many new topological insulating and superconducting materials, leading to beautiful experimental confirmations of fundamental mathematical ideas, and opening the door to harnessing their robust properties in microelectronic, optical, and quantum information processing devices. The main goal of the proposed research is to extend this systematic understanding of universal topological phases and phase transitions that arise in i) solid-state devices driven far out of thermal equilibrium by time-dependent forcing, ii) noisy quantum circuit dynamics found in emerging quantum computing processors, and iii) conducting (gapless) phases of matter underlying longstanding mysteries of condensed matter physics such as the origins high-temperature superconductivity and strange metal behavior. This work will address fundamental questions about both the types of quantum phases of matter that can arise in nature, and the fundamental capabilities and limitations of using noisy and imperfect quantum systems for quantum computation. This understanding will, in turn, be used to design robust methods to dynamically control the correlations and entanglement in electronic devices and quantum computers that are insensitive to control errors and other sources of noise and imperfections that form key bottlenecks for current quantum technology.