Supersymmetry in strongly correlated fermion models

Yoshio Kuramoto

Arianna Montorsi, Mario Rasetti, A. I. Solomon

M. D. Gould, Yao-Zhong Zhang, Huan-Qiang Zhou

An integrable eight-state supersymmetric $U$ model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has a $gl(3|1)$ supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained.

Raoul Santachiara, Kareljan Schoutens

In a recent work, N = 2 supersymmetry has been proposed as a tool for the analysis of itinerant, correlated fermions on a lattice. In this paper, we extend these considerations to the case of lattice fermions with spin 1/2. We introduce a model for correlated spin-1/2 fermions with a manifest N = 4 supersymmetry, and analyse its properties. The supersymmetric ground states that we find represent holes in an anti-ferromagnetic background.

Christian Hagendorf, Thessa Fokkema, Liza Huijse

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the $\mathcal N=1$ super-sine-Gordon model at a particular coupling where an additional $\mathcal N=(2,2)$ supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.

José M. Arias, María Isabel Gallardo, Manuel Lozano