Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality

Abstract

We study a model for itinerant, strongly interacting fermions where a judicious tuning of the interactions leads to a supersymmetric Hamiltonian. On the triangular lattice this model is known to exhibit a property called superfrustration, which is characterized by an extensive ground state entropy. Using a combination of numerical and analytical methods we study various ladder geometries obtained by imposing doubly periodic boundary conditions on the triangular lattice. We compare our results to various bounds on the ground state degeneracy obtained in the literature. For all systems we find that the number of ground states grows exponentially with system size. For two of the models that we study we obtain the exact number of ground states by solving the cohomology problem. For one of these, we find that via a sequence of mappings the entire spectrum can be understood. It exhibits a gapped phase at 1/4 filling and a gapless phase at 1/6 filling and phase separation at intermediate fillings. The gapless phase separates into an exponential number of sectors, where the continuum limit of each sector is described by a superconformal field theory.

50 pages, 12 figures, 2 appendices

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• Quench Dynamics in Two-Dimensional Integrable SUSY Models
• Density-matrix based numerical methods for discovering order and correlations in interacting systems
• Designs of magnetic atom-trap lattices for quantum simulation experiments
• Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs
• Ground states of Nicolai and ${\mathbb{Z}}_2$ Nicolai models
• Supersymmetry and multicriticality in a ladder of constrained fermions
• A Novel Perspective on Ideal Chern Bands with Strong Short-Range Repulsion: Applications to Correlated Metals, Superconductivity, and Topological Order
• Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls
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• Supersymmetry dynamics on Rydberg atom arrays
• Construction of an algebra corresponding to a statistical model of the square ladder (square lattice with two lines)