Tensor network models of AdS/qCFT
arXiv:2004.04173 · doi:10.22331/q-2022-02-03-643
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.
arXiv comment12 pages, 8 figures (journal version)
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Cited by in corpus (8)
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- 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
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- Entanglement distillation toward minimal bond cut surface in tensor networks
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