  We discuss the reformulation of the O(2) model with a chemical potential and
the Abelian Higgs model on a 1+1 dimensional space-time lattice using the
Tensor Renormalization Group (TRG) method. The TRG allows exact blocking and
connects smoothly the classical Lagrangian approach to the quantum Hamiltonian
approach. We calculate the entanglement entropy in the superfluid phase of the
O(2) model and show that it approximately obeys the logarithmic Calabrese-Cardy
scaling obtained from Conformal Field Theory (CFT). We calculate the Polyakov
loop in the Abelian Higgs model and discuss the possibility of a deconfinement
transition at finite volume. We propose Bose-Hubbard Hamiltonians implementable
on optical lattices as quantum simulators for CFT models.
