Phase transitions of a two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki model

We study spin-2 deformed-AKLT models on the square lattice, specifically a two-parameter family of O(2)-symmetric ground-state wave functions as defined by Niggemann, Klümper, and Zittartz, who found previously that the phase diagram consists of a Néel-ordered phase and a disordered phase which contains the AKLT point. Using tensor-network methods, we not only confirm the Néel phase but also find an XY phase with quasi-long-range order and a region adjacent to it, within the AKLT phase, with very large correlation length, and investigate the consequences of a perfectly factorizable point at the corner of that phase.