Relativistic fermions in Flatland: from moiré materials to gauge field theories

Planar fermions underpin much interesting physics 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. More recently, layered structures exhibiting moiré patterns—arising from slight rotational misalignments or lattice constant mismatches between individual layers—have emerged as highly tunable platforms for studying interacting relativistic fermion systems. Quantum fermions in 2+1d also present many theoretical challenges, and there is an encouraging parallel renaissance of interest involving among others workers in large loop-order perturbation theory, functional renormalisation group, conformal bootstrap, and lattice simulation, for whose practitioners such systems encapsulate essential challenges for their respective agendas. Another recent promising technique is quantum simulation, which is particularly suited for dynamics due to its use of unitary operations. Current digital quantum hardware available for cloud computing offers on the order of a hundred physical qubits, with analog computers offering on the order of a thousand qubits. These numbers are promising for out-of-equilibrium simulations of planar systems, and theoretical progress has been made for algorithms involving computers based on fermionic components rather than the usual bosonic qubits, which holds promise for efficient fermionic simulations. A week-long workshop hosted at ECT* is a perfect forum to assemble attendees spanning this diverse community, stimulate knowledge exchange, and spawn fresh research directions.