Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality

TL;DR

This paper investigates a supersymmetric fermion model on the triangular lattice, revealing superfrustration with extensive ground state entropy, and identifies critical phases with exact ground state counts and superconformal field theory descriptions.

Contribution

It provides a detailed analysis of superfrustration in a supersymmetric lattice fermion model, including exact ground state enumeration and spectrum characterization.

Findings

Ground state degeneracy grows exponentially with system size.

Identified gapped and gapless phases at different fillings.

Spectrum exhibits superconformal field theory sectors.

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.