Tensor network models of AdS/qCFT

Abstract

The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.

12 pages, 8 figures (journal version)

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Cited by in corpus (8)

• Holographic tensor network models and quantum error correction: A topical review
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
• Path-Integral Optimization from Hartle-Hawking Wave Function
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Boundary theories of critical matchgate tensor networks
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Understanding holographic error correction via unique algebras and atomic examples