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The strongly-correlated behavior of electrons in low dimensional systems, such as graphene, fullerenes, nanoribbons and nanotubes, require non-perturbative methods ideally suited for lattice QMC. I discuss how QMC is used to simulate these low-dimensional systems to ascertain their electronic properties. At the same time, I show how the relatively small dimensions of these systems offer ideal platforms for developing novel algorithms, such as "contour deformations" and "radial updates". The former alleviates the sign problem, allowing for simulations at non-zero chemical potential, while the latter removes ergodicity issues and thus mitigates critical slowing down. Finally I discuss how QMC methods can be used to investigate the topological properties of these systems, which could have impact in their usage as novel quantum devices.
Wolfgang Unger