Lattice Models with N=2 Supersymmetry

TL;DR

This paper introduces lattice models with explicit N=2 supersymmetry, connecting them to conformal field theory, Bethe ansatz, and cohomology, and explores their ground states and generalizations.

Contribution

It presents the first explicit lattice models with N=2 supersymmetry, linking them to various theoretical frameworks and analyzing their ground-state properties.

Findings

Models exhibit supersymmetry on arbitrary graphs.

Ground-state structure analyzed on complex graphs like ladders.

Provides a supersymmetric lattice regulator for the Thirring model.

Abstract

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q^+ and Q^- yield the Hamiltonian H={Q^+,Q^-} on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers. The Hamiltonian of our simplest model contains a hopping term and a repulsive potential, as well as the hard-core repulsion. We discuss these models from a variety of perspectives: using a fundamental relation with conformal field theory, via the Bethe ansatz, and using cohomology methods. The simplest model provides a manifestly-supersymmetric lattice regulator for the supersymmetric point of the massless 1+1-dimensional Thirring (Luttinger) model. We discuss the ground-state structure of this same model on more complicated graphs, including a 2-leg ladder, and discuss some generalizations.