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.

Kink dynamics and quantum simulation of supersymmetric lattice Hamiltonians

“…We note that a similar proposal has appeared in the form of a conference abstract [45,46]. Our results constitute a stepping stone to quantum simulations of supersymmet-ric lattice models in higher dimensions [18,[47][48][49][50], which can require n-body, rather than 2-body, interactions. In this context, it would be interesting to consider a recently proposed scheme relying on coupling the Rydberg atoms with phonons [51] or to use cold molecules with permanent or electric-field induced dipole moments, avoiding the need for off-resonant dressing [52][53][54][55].…”

Density-matrix based numerical methods for discovering order and correlations in interacting systems

“…In addition, the Hamiltonian includes the usual nearest-neighbor hopping and chemical potential terms: the supersymmetry holds when all three terms have the same coefficients. From our viewpoint here, the outstanding feature of the model is that for a range of fillings (about 1/7 to 1/5 in the triangular lattice case), there is a large-ground state degeneracy [49,50] (all of them with exactly zero energy) and the entropy is extensive. To date, there is no field theory for this phase and practically nothing is understood about it: is it a like a Hall fluid, an ordered density-wave, a Kosterlitz-Thouless critical phase?…”

“…This model is very favorable to ED as the combined restrictions of no spin and no neighbors reduces the Hilbert dimension [48] so the attainable system size is 3 − 4 times that for a Hubbard model, approaching 50 sites (as studied in Ref. [49]). …”

Kink Dynamics and Quantum Simulation of Supersymmetric Lattice Hamiltonians

“…Outlook.-We have proposed a realization of a supersymmetric lattice Hamiltonian H Q based on atoms interacting through a Rydberg dressed potential [82,83]. Our results constitute a stepping stone to quantum simulations of supersymmetric lattice models in higher dimensions [18,[84][85][86][87], which can require n-body, rather than twobody, interactions. In this context, it would be interesting to consider a scheme relying on coupling the Rydberg atoms with phonons [88] or to use cold molecules with permanent or electric-field-induced dipole moments, avoiding the need for off-resonant dressing [45][46][47][48].…”