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Time evolution of the quantum Ising model in two dimensions using tree tensor networks

Wladislaw Krinitsin1,2,*, Niklas Tausendpfund1,3, Markus Heyl4,5, Matteo Rizzi1,3, and Markus Schmitt1,2

  • *Contact author: w.krinitsin@fz-juelich.de
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Phys. Rev. B 112, 134310 – Published 17 October, 2025

DOI: https://doi.org/10.1103/kj16-sqcm

Abstract

The numerical simulation of two-dimensional quantum many-body systems away from equilibrium constitutes a major challenge for all known computational methods. We investigate the utility of tree tensor network (TTN) states to solve the dynamics of the quantum Ising model in two dimensions. Within the perturbative regime of small transverse fields, TTNs faithfully reproduce analytically known, but nontrivial and physically interesting dynamics of magnetic domains, for lattices up to 16×16 sites. Limitations of the method related to the rapid growth of entanglement entropy are explored within more general, paradigmatic quench settings. We provide and discuss comprehensive benchmarks regarding the benefit of GPU acceleration and the impact of using local operator sums on the performance.

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Phys. Rev. B 112, 134310– Published 17 October, 2025
  • Received 13 June 2025
  • Revised 8 September 2025
  • Accepted 29 September 2025
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