Order and supersymmetry at high filling zero-energy states on the triangular lattice

• Main Authors: Galanakis, Dimitrios., Papanikolaou, S., Henley, Christopher L.
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2013
• Subjects: DRNTU::Science::Chemistry::Physical chemistry
• Online Access: https://hdl.handle.net/10356/95393; http://hdl.handle.net/10220/9337
• Institution: Nanyang Technological University

We perform exact-diagonalization studies in d=2 dimensions for the Fendley and Schoutens model of hard-core and nearest-neighbor-excluding fermions that displays an exact nonrelativistic supersymmetry. Using clusters of all possible shapes up to 46 sites, we systematically study the behavior of the ground-state phase diagram as a function of filling. We focus on the highly degenerate zero-energy states found at fillings between 1/7 and ∼1/5. At the lower end of that interval, at filling 1/7, we explicitly show that the ground states are gapped crystals. Consistent with previous suggestions, we find that the extensive entropy of zero states peaks at a filling of ∼0.178. At the higher end of the interval, we find zero-energy ground states at fillings above 1/5, contrary to previous expectations, which display nontrivial amplitude degeneracies.