  We discuss the Tensor Renormalization Group (TRG) method for the O(2) model
with a chemical potential in 1+1 dimensions with emphasis on near
gapless/conformal situations. We emphasize the role played by the late Leo
Kadanoff in the development of this theoretical framework. We describe the
entanglement entropy in the superfluid phase (see arXiv:1507.01471 for
details). We present recent progress on optimized truncation methods.
