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Quantum Ising Model on(2+1)- Dimensional Anti - de Sitter Space using Tensor Networks
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Quantum Ising Model on(2+1)- Dimensional Anti - de Sitter Space using Tensor Networks

Simon Catterall, Alexander F Kemper, Yannick Meurice, Abhishek Samlodia and Goksu Can Toga
ArXiv.org
Cornell University
12/23/2025
DOI: 10.48550/arxiv.2512.20838
url
https://doi.org/10.48550/arxiv.2512.20838View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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). Our spatial lattices correspond to regular tessellations of hyperbolic space with coordination number seven. We find the ground state of this model using the Density Matrix Renormalization Group (DMRG) algorithm which allowed us to probe lattices that range in size up to 232 sites. We explore the bulk phase diagram of the theory 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 the anti-de Sitter background. By tracing out the bulk indices, we are able to compute the density matrix for the boundary theory. At the critical point, we find the entanglement entropy exhibits the logarithmic dependence of boundary length expected for a one-dimensional CFT 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 highly connected systems. We also measure Out-of-time-Ordered-Correlators (OTOCs) to explore the scrambling behavior of the theory.
 Physics - High Energy Physics - Lattice Physics - High Energy Physics - Theory Physics - Quantum Physics

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