Intermediate scale phenomena in cuprates

After 20 years of research the low energy physics of cuprates remains a mystery. It is generally accepted that a three band Hamiltonian with Cu's and O's orbitals should contain the essential physics so we can say that there is consensus at the length scale of the Cu-O distance but there is disagreement when it comes to describe higher length scales or to set up a low energy model. Here we present computations of cuprates which accurately describe the physics arising at scales of up to several lattice constants. We review the comparison of our results with different proves as resonant X-ray scattering, scanning tunneling microscopy, optical conductivity and magnetic neutron scattering.