One of the hottest topics on cold atoms is quantum simulation of strongly correlated many-body systems with optical lattices We need precision analysis of current optical lattice experiments for strictly testing strong-correlation theories We can improve precision by improving numerical and analytical technologies But good understanding of optical lattices could be one essential step, which has not been discussed beforeOne of the hottest topics on cold atoms is quantum simulation of strongly correlated many-body systems with optical lattices . We need precision analysis of current optical lattice experiments for strictly testing strong-correlation theories. good understanding of optical lattices could be one essential step, which has not been discussed before. We can improve precision by improving numerical and analytical technologies. But