Melting and boiling points increase further down the halogen group, but they decrease further down the alkali metal group. I know that the former's trend has to do with the van der Waals force, but I don't understand why it is not applied to the alkali metal group. Please explain why the halogens are affected by the van der Waals force and the alkali metals are not.
Because, in the condensed phases, you don't have molecules of metallic elements. You have, as a first approximation, a "rice pudding" structure where cations are embedded (like raisins) in a "pudding" of delocalized valence electrons (metallic bonding). The main cohesive force in the condensed metals is then electrostatic attraction between the opposing charges of the cations and electrons. In alkali metals where each atom breaks up into the same charge cation (+1 charge) and produces the same number of delocalized electrons (one per atom), this electrostatic attraction goes down with larger atoms.