Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks
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arXiv
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| Format: | Preprint |
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2025
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| author | Samlodia, Abhishek Catterall, Simon Kemper, Alexander F. Meurice, Yannick Toga, Goksu Can |
| author_facet | Samlodia, Abhishek Catterall, Simon Kemper, Alexander F. Meurice, Yannick Toga, Goksu Can |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks Samlodia, Abhishek Catterall, Simon Kemper, Alexander F. Meurice, Yannick Toga, Goksu Can High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics 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. |
| title | Quantum Ising Model on $(2+1)-$Dimensional Anti$-$de Sitter Space using Tensor Networks |
| topic | High Energy Physics - Lattice High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2512.20838 |