Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 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 {\it 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 $D\to \mathrm{\infty }$. Recent advances in variational optimization and scaling based on correlation lengths demonstrated the ability of iPEPS to capture the spontaneous breaking of a continuous symmetry in phases such as the antiferromagnetic (Néel) phase 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 $S=1\mathrm{/}2$ 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.