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 study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble using Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value 0.1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes noncritical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square lattice problem.