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

Abstract

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 non-relativistic 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, in contradiction to previous numerical studies and analytical suggestions; these display non-trivial amplitude degeneracies.

10 pages, 7 figures, 2 tables

References in corpus (6)

• Topological Order and Conformal Quantum Critical Points
• Emergence of supersymmetry at a critical point of a lattice model
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Charge frustration and quantum criticality for strongly correlated fermions
• Extensive ground state entropy in supersymmetric lattice models
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Cited by in corpus (5)

• A supersymmetric multicritical point in a model of lattice fermions
• Density-matrix based numerical methods for discovering order and correlations in interacting systems
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Supersymmetry and multicriticality in a ladder of constrained fermions
• Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls