Phase transitions of a 2D deformed-AKLT model

We study deformed-AKLT models on the square lattice, via a two-parameter family of $O(2)$-symmetric ground-state wavefunctions as defined by Niggemann, Kl\"umper, and Zittartz, who found previously that the phase diagram consists of a N\'eel-ordered phase and a disordered phase which contains the AKLT point. Using tensor-nework methods, we not only confirm the N\'eel phase but also find an XY phase with quasi-long-range order, and investigate the consequences of a seemingly isolated product-state point at the boundary of the phase diagram.