Aspects of Strongly-Inetracting Quantum Fiueld Theory in Three Spacetime Dimensions

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Planar fermions occur frequently in layered systems and are extensively studied in condensed matter physics; for instance, electronic properties of graphene have long been understood in terms of relativistic fermions centred on Dirac points in momentum space, but the influence of interactions between charge-carrying degrees of freedom is less well-understood and remains an active field of study. Quantum fermions in 2+1d also present many theoretical challenges, since there is often no natural small parameter permitting a controlled approximation, and there is a renaissance of interest involving among others workers in functional renormalisation group, conformal bootstrap, and lattice simulation, tools mainly developed for particle theory, for whose practitioners such systems encapsulate essential challenges for their respective agendas.This project will build on recent work developing lattice field theory techniques for simulating interacting planar systems with the correct global symmetries intrinsic to relativistic fermions, using insight from the Domain Wall Fermion formulation originally developed for precision studies in Quantum Chromodynamics. Issues to be addressed:How can we control the calculation of strongly-interacting dynamics, and have confidence to apply it to realistic condensed matter problems? Are there lattice formulations yielding the expected continuum symmetries in some limit? Can we extend our methods away from half-filling?What is the critical number of species below which quantum critical points associated with dynamical gap generation can occur? What is the nature of the corresponding continuum quantum field theory? What are its symmetries? Is it local?The project will exploit both Supercomputing