  We present a full identification of lattice model properties with their field
theoretical counter parts in the continuum limit for a supersymmetric model for
itinerant spinless fermions on a one dimensional chain. The continuum limit of
this model is described by an $\mathcal{N}=(2,2)$ superconformal field theory
(SCFT) with central charge c=1. We identify states and operators in the lattice
model with fields in the SCFT and we relate boundary conditions on the lattice
to sectors in the field theory. We use the dictionary we develop in this paper,
to give a pedagogical explanation of a powerful tool to study supersymmetric
models based on spectral flow. Finally, we employ the developed machinery to
explain numerically observed properties of the particle density on the open
chain presented in Beccaria et al. PRL 94:100401 (2005).
