Order of the phase transition in the infinite bond dimension limit

Determine whether the anisotropy-driven phase transition between the SU(4) plaquette-singlet phase and the Néel–valence-bond-crystal coexisting phase in the SU(4) antiferromagnetic Heisenberg model on a square plaquette lattice is continuous or first-order in the limit of infinite iPEPS bond dimension, and ascertain the nature of the transition at large bond dimensions.

Background

The paper studies the SU(4) antiferromagnetic Heisenberg model on a square plaquette lattice with intra- and inter-plaquette interactions J and J'. Using iPEPS, the authors find an SU(4) singlet ground state in the strongly anisotropic regime (small J'/J) and a Néel–VBC coexisting ground state near the isotropic limit (J'/J≈1), with a transition around J'/J≈0.85.

For bond dimensions D=7–12, a level crossing between the two states is observed, suggesting a likely first-order transition. However, the authors explicitly note that in the infinite bond dimension limit they cannot rule out a continuous transition and state that determining the nature of the transition at larger bond dimensions is left for future paper.