Lattice Supersymmetry from the Ground Up

Fendley, Paul; Schoutens, Kareljan

doi:10.1007/978-90-481-2810-5_19

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“…Thus the addition energies show an even/odd alternation on top of an overall increasing trend, due to the repulsive (hardcore) interaction. If it were necessary to incorporate interaction effects in a systematic way, one relatively simple The degeneracy of the zero-energy states is best characterized by their zero state entropy 18 , which is extensive in the intermediate fillings. This fact suggests that at the infinite system size limit, the wave function incorporates a mix of local patterns (especially fragments of the crystals in Figure 2.…”

Section: Results: Phase Diagrammentioning

confidence: 99%

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

2012

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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.

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Section: Results: Phase Diagrammentioning

confidence: 99%