Studying XY-like critical phases using tensor-network renormalization

The development of 2D tensor renormalization techniques capable of isolating short-range correlations, such as Evenbly and Vidal's tensor network renormalization (TNR) and Yang, Gu, and Wen's loop-TNR, offers us non-perturbative numerical tools to analyze long-distance behavior of systems with large or infinite correlation length. We test these methods on systems with continuously-varying criticality, in particular, systems which behave in the infrared as a c=1 free-boson CFT. Exactly-solved models with this property, in particular the six-vertex model and the spin-½ XXZ chain, allow us to benchmark the precision of these methods. We also examine classical Z_N spin models, which are not exactly solvable but which are known to have "soft" phases with physics resembling that of the low-temperature XY model. We study these phases and interpret our results in light of their Kramers-Wannier duality, using methods developed by Hauru et al. (2016).