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

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 genericpurpose 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 Neel phase for J(2)/J(1) <= 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 approximate to) 0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

Automated summary

The recent progress in the optimization of two-dimensional tensor networks based on automatic differentiation has allowed for the precise and fast optimization of states like infinite projected entangled-pair states (iPEPS). By studying the J(1)-J(2) Heisenberg antiferromagnet model on the square lattice, accurate estimations of the magnetization curve in the Neel phase have been reported. The methodology used in this work can be extended to study generic order-to-disorder transitions in magnetic systems.