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Diagonal isometric form for tensor network states in two dimensions

Benjamin Sappler1,2,*, Masataka Kawano1,2, Michael P. Zaletel3,4, and Frank Pollmann1,2

  • *Contact author: benjamin.sappler@tum.de
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Phys. Rev. B 113, 165117 – Published 10 April, 2026

DOI: https://doi.org/10.1103/56px-qsxx

Abstract

Isometric tensor network states (isoTNS) generalize the isometric form of the one-dimensional matrix product states to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTNS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTNS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTNS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome lattice.

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23 July, 2026

Correction: A missing funding support statement has been added.

Article Text

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Phys. Rev. B 113, 165117– Published 10 April, 2026
  • Received 13 October 2025
  • Accepted 25 February 2026
  • Corrected 23 July 2026
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