Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-½ ladders

Infinite projected entangled-pair states (iPEPS) have been introduced to accurately describe many-body wave functions on two-dimensional lattices. In this context, two aspects are crucial: the systematic improvement of the Ansatz by the optimization of its building blocks, i.e., tensors characterized by bond dimension D, and the extrapolation scheme to reach the “thermodynamic” limit D→∞. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture phases with spontaneously broken continuous symmetry such as the antiferromagnetic (Néel) one with high fidelity, in addition to valence-bond solids which are already well described by finite-D iPEPS. In contrast, systems in the vicinity of continuous quantum phase transitions still present a challenge for iPEPS, especially when non-Abelian symmetries are involved. Here, we consider the iPEPS Ansatz to describe the continuous transition between the (gapless) antiferromagnet and the (gapped) paramagnet that exists in the S=1/2 Heisenberg model on coupled two-leg ladders. In particular, we show how accurate iPEPS results can be obtained down to a narrow interval around criticality and analyze the scaling of the order parameter in the Néel phase in a spatially anisotropic situation.