Paul Fendley

Abstract:

Lattice models with N = 2 supersymmetry are introduced. It is shown that the continuum limit of the simplest of these models is a well known (1 + 1)-dimensional quantum field theory with N = (2,2) superconformal symmetry. The close connections with models of current interest in the study of strongly correlated electrons is noted. Furthermore, it is demonstrated how supersymmetry can be useful in studying their properties.

Abstract:

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators 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. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.