Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

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 $9$, 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 $Ansatz$ 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 Néel 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.

12 pages, 9 figures, source code available at https://github.com/jurajHasik/peps-torch

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