Lattice fermion models with supersymmetry

TL;DR

This paper explores lattice fermion models with N=2 supersymmetry, revealing their special properties, solutions via Bethe ansatz, and connections to well-known spin chains and superconformal models.

Contribution

It introduces and analyzes supersymmetric lattice fermion models, providing Bethe ansatz solutions and linking them to established integrable systems and conformal theories.

Findings

Bethe ansatz solutions for the simplest models

Connections to XXZ and tJ models at specific parameters

Models include critical points described by superconformal minimal models

Abstract

We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k=1 model with the spin-1/2 antiferromagnetic XXZ chain at \Delta=-1/2, and the k=2 model with both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at \Delta=-1/\sqrt{2}. We argue that these models include critical points described by the superconformal minimal models.