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Abstract

In recent years a new paradigm has emerged to investigate non-Fermi liquids without quasiparticles, based on the exactly-solvable Sachdev-Ye-Kitaev model which consists of a large number of fermions with all-to-all, random Gaussian interactions. This model exhibits a rich phenomenology at low energy, including power-law decaying spectral functions, maximal chaos and connections to black hole horizons in anti-de Sitter spacetime. These intriguing properties have inspired a broad research program at the intersection of condensed matter physics, quantum information and quantum gravity. In this thesis we explore the phases and phase transitions occurring in Sachdev-Ye-Kitaev models that are coupled in various ways, with an eye on physical platforms that could enable their realization in condensed matter systems. This journey takes us from the investigation of quantum chaos in many-body systems and revival dynamics in traversable wormholes, all the way to the physics of disordered graphene flakes and unconventional superconductivity.