Abstract
Liza Huijse (University of Amsterdam, the Netherlands)
Quantum phases of a supersymmetric model of lattice fermions
We review recent results, obtained with K. Schoutens and P. Fendley, on frustration of quantum charges in lattice models for itinerant fermions with strong repulsive interactions. A judicious tuning of kinetic and potential terms leads to models possessing supersymmetry. In 1D this model is solved analytically and turns out to be quantum critical. The thermodynamic limit is described by an N=2 superconformal field theory. In 2D the model exhibits superfrustration: an extensive degeneracy of supersymmetric ground states. Using techniques from cohomology the ground state degeneracy can be obtained analytically. We demonstrate how for the 2D square lattice the ground state counting problem is fully solved through a remarkable correspondence with specific rhombus tilings of the plane.