A case study of emergent gravity in a model of randomly hopping fermions (2016)

Undergraduate: Jonathan Schirmer

Faculty Advisor: Dmitri Khveshchenko
Department: Physics & Astronomy

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For years, new microscopic models have been sought in order to explore and test holographic duality. Following solvable examples in string theory, many studies have focused on models of strongly coupled quantum systems which display emergent symmetries. Connections have then been made with holographic models which display similar symmetric properties. By matching propagators, insight can be gained about the thermodynamics of the strongly coupled quantum system or its holographic dual. In this study, we explore and generalize a specific example involving the random hopping of fermions across discrete sites, which is found to possibly be dual to AdS2 horizons of extremal charged black holes. We generalize the power law associated with the self-energy and determine how this affects the thermodynamics on either side of the duality. Finally, we attempt to construct the generalized model from a microscopic Hamiltonian.