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.

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

Becca, F
2021

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 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/3028870
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