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Variational optimization of projected entangled-pair states on the triangular lattice

Jan Naumann1, Jens Eisert1,2, and Philipp Schmoll1

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Phys. Rev. B 113, 045117 – Published 9 January, 2026

DOI: https://doi.org/10.1103/g5gm-tzf8

Abstract

We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbor interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbor Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.

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Phys. Rev. B 113, 045117– Published 9 January, 2026
  • Received 17 October 2025
  • Accepted 11 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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