# BEC in interacting systems

What is your thought on the following statement: "any system of (weak/ strong) interacting bosons, in liquid phase, will form a condensate at T=0". Any example or counter-example ? Will dimensionality play any role? Thanks!

• Many counter examples. In one spatial dimension there is no spontaneous symmetry breaking at $T=0$. In two dimensions, interacting bosons in a lattice can form a Mott insulator. – Meng Cheng Sep 12 '15 at 0:45