Tensor RG calculations and quantum simulations near criticality

Understand

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.