Field theory on a lattice: Absence of goldstone bosons in the U(1) model in two dimensions

Abstract
We study the U(1)-Goldstone model in two dimensions. We formulate this model on a one-dimensional spatial lattice and show that Coleman's theorem (i.e., there exist no Goldstone bosons in two dimensions) is satisfied by the solution found by the variational approach of dissecting the lattice into small (4-site) blocks and iteratively constructing an effective truncated Hamiltonian.