  The Hatsugai-Kohmoto interaction model has gained a lot of attention in
recent years, due to the fact it is exactly solvable in momentum space in any
dimension while capturing some key features of the Mott phase. Here a
one-dimensional lattice model with this interaction is approached from the
real-space perspective, to explore how breaking the translation invariance of a
lattice affects the intuition built by studying the exact solution in
$k$-space. The ground state properties of chains with periodic and open
boundary conditions are calculated and compared with both the exact solution in
momentum space, as well as with analogous solutions of the Hubbard model. The
results show that introducing hard edges enhances the ferromagnetic
correlations and the system undergoes a magnetic transition before reaching the
strong coupling limit. Understanding the impact of hard edges is a crucial step
toward answering the looming question of the existence of edge states and other
topological phenomena in systems with this type of interaction.
