Symmetric projected entangled-pair states analysis of a phase transition in coupled spin-1/2 ladders

TL;DR

This paper uses symmetric iPEPS to analyze a quantum phase transition in coupled spin-1/2 ladders, demonstrating accurate results near criticality and exploring order parameter scaling in an anisotropic setting.

Contribution

It introduces a symmetric iPEPS approach to study continuous phase transitions in coupled spin ladders, addressing challenges near critical points with non-abelian symmetries.

Findings

Accurate iPEPS results near the critical point.

Scaling behavior of the order parameter in anisotropic conditions.

Effective description of the transition between antiferromagnetic and paramagnetic phases.

Abstract

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 $D \to \infty$. 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 (N\'eel) 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 $S=1/2$ 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 N\'eel phase in a spatially anisotropic situation.