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

Juraj Hasik, Didier Poilblanc, Federico Becca

SciPost Phys. 10, 012 (2021) · published 20 January 2021

- doi: 10.21468/SciPostPhys.10.1.012
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### 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 an- tiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we re- port accurate estimations of the magnetization curve in the Néel 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 ≈ 0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

### Cited by 37

### Authors / Affiliations: mappings to Contributors and Organizations

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^{1}Juraj Hasik, -
^{1}Didier Poilblanc, -
^{2}Federico Becca

^{1}Laboratoire de Physique Théorique Toulouse [LPT]^{2}Università degli Studi di Trieste / University of Trieste [UNITS]