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Dirty Quantum Criticality

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Many of the most mysterious phenomena in condensed matter physics involve systems near quantum phase transitions where the interplay of quenched disorder and strong interactions likely plays an essential role. Examples include the appearance of "anomalous" 2d metallic phases and the sharing of critical exponents between seemingly different quantum Hall plateau transitions. However, few organizing principles have been developed for understanding quantum critical systems with interactions and disorder, and analytically tractable models have proven rare. In this talk, I will describe some of the first examples of quantum critical theories in 2d characterized by finite disorder and interaction strengths, focusing on particular examples of quenched disorder in systems of (i) Dirac fermions coupled to an emergent gauge field (QED3) and (ii) scalar bosons at their Wilson-Fisher fixed point. Both of these examples exhibit universal features not found together in systems with interactions or disorder alone, such as vanishing density of states, finite DC conductivities, and novel critical exponents.