Tensor network models of AdS/qCFT

Jahn A, Zimboras Z, Eisert J (2022)

Publication Type: Journal article

Publication year: 2022


Book Volume: 6

Pages Range: 643-

DOI: 10.22331/Q-2022-02-03-643


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.

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How to cite


Jahn, A., Zimboras, Z., & Eisert, J. (2022). Tensor network models of AdS/qCFT. Quantum, 6, 643-. https://doi.org/10.22331/Q-2022-02-03-643


Jahn, Alexander, Zoltan Zimboras, and Jens Eisert. "Tensor network models of AdS/qCFT." Quantum 6 (2022): 643-.

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