Investigation of the N\'eel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

TL;DR

This paper uses advanced differentiable tensor network techniques to accurately study the Ne9el phase of the frustrated J1-J2 Heisenberg antiferromagnet, identifying the phase transition point with high precision.

Contribution

It introduces a novel application of differentiable symmetric tensor networks to analyze the J1-J2 model, providing precise estimates of the phase transition and magnetic order.

Findings

Ne9el order vanishes at J2/J1 b1 0.46

Identified and imposed U(1) symmetry in tensor networks

Accurate magnetization curve in the Ne9el phase

Abstract

The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X ${\bf 9}$, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose ${\it Ansatz}$ for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the $J_1-J_2$ Heisenberg antiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we report accurate estimations of the magnetization curve in the N\'eel phase for $J_2/J_1 \le 0.45$. The unrestricted iPEPS simulations reveal an $U(1)$ symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at $J_2/J_1 \approx 0.46(1)$. The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.