SciPost Phys. 10, 012 (2021) ·
published 20 January 2021
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· pdf
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.
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in Submissions | report on Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks