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We study a model of spinless fermions on the honeycomb lattice withnearest-neighbor exclusion and extended repulsive interactions that exhibits`lattice supersymmetry' [P. Fendley, K. Schoutens, and J. de Boer, Phys. Rev.Lett. 90, 120402 (2003)]. Using a combination of exact diagonalization of large($N\leq56$ site) systems, mean-field numerics, and symmetry analysis, weestablish a rich phase structure as a function of fermion density, thatincludes non-Fermi liquid behavior, resonating charge stripes, domain-wall andbubble physics, and identify a finite range of fillings with extensive groundstate degeneracy and both gapped and gapless spectra. We comment on thestability of our results to relaxing the stringent requirements forsupersymmetry, and on their possible broader relevance to systems ofstrongly-correlated electrons with extended repulsive interactions.

Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls