Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls

TL;DR

This paper investigates a honeycomb lattice model of spinless fermions with supersymmetry, revealing complex phases including charge stripes, domain walls, and extensive degeneracy, using numerical and analytical methods.

Contribution

It provides the first detailed analysis of supersymmetric fermion models on the honeycomb lattice, uncovering rich phase structures and degeneracies.

Findings

Identification of non-Fermi liquid behavior

Discovery of resonating charge stripes and domain walls

Extensive ground state degeneracy with gapped and gapless spectra

Abstract

We study a model of spinless fermions on the honeycomb lattice with nearest-neighbor exclusion and extended repulsive interactions that exhibits `lattice supersymmetry' [P. Fendley, K. Schoutens, and J. de Boer, Phys. Rev. Lett. 90, 120402 (2003)]. Using a combination of exact diagonalization of large ($N\leq56$ site) systems, mean-field numerics, and symmetry analysis, we establish a rich phase structure as a function of fermion density, that includes non-Fermi liquid behavior, resonating charge stripes, domain-wall and bubble physics, and identify a finite range of fillings with extensive ground state degeneracy and both gapped and gapless spectra. We comment on the stability of our results to relaxing the stringent requirements for supersymmetry, and on their possible broader relevance to systems of strongly-correlated electrons with extended repulsive interactions.