Enhanced compressibility due to repulsive interaction in the Harper model

We study the interplay between a 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 the density matrix renormalization group, we find that, in contrast to standard behavior, the system becomes more compressible as the repulsive interaction is increased. By deriving 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 anticorrelated 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.