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Solvable models of correlated metals with interactions and disorder, and their transport properties

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Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature 

superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic 

phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional

perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the 

solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will 

describe constructions of solvable models of strange metals based on SYK-like large-N limits, which can reproduce  

some of the experimentally observed features of strange metals and adjoining phases. These models, and further 

extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building 

blocks of the electronic state in correlated-electron superconductors near optimal doping.