  We study the interplay between repulsive interaction and an almost staggered
on-site potential in one-dimension. Specifically, we address the Harper model
for spinless fermions with nearest-neighbor repulsion, close to half-filling.
Using density matrix renormalization group (DMRG), we find that, in contrast to
standard behavior, the system becomes more compressible as the repulsive
interaction is increased. By generating a low-energy effective model, we unveil
the effect of interactions using mean-field analysis: the density of a narrow
band around half-filling is anti-correlated with the on-site potential, whereas
the density of lower occupied bands follows the potential and strengthens it.
As a result, the states around half-filling are squeezed by the background
density, their band becomes flatter, and the compressibility increases.
