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Quantum Ising model on (2+1)-dimensional anti–de Sitter space using tensor networks

Abhishek Samlodia1,*, Simon Catterall1,†, Alexander F. Kemper2,‡, Yannick Meurice3,§, and Goksu Can Toga2,∥

  • *Contact author: asamlodi@syr.edu
  • †Contact author: smcatter@syr.edu
  • ‡Contact author: akemper@ncsu.edu
  • §Contact author: yannick-meurice@uiowa.edu
  • ∥Contact author: gctoga@ncsu.edu
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Phys. Rev. D 113, 114507 – Published 10 June, 2026

DOI: https://doi.org/10.1103/9rtx-95s6

Abstract

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using matrix product states (MPS) and matrix product operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space with coordination number seven and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with holography. At the critical point, we find the boundary entanglement entropy scales logarithmically with subsystem size but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and/or highly connected systems. We also measure out of time ordered correlators (OTOCs) to explore the scrambling behavior of the theory.

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Phys. Rev. D 113, 114507– Published 10 June, 2026
  • Received 10 April 2026
  • Accepted 7 May 2026
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