Tensor network models of AdS/qCFT
- URL: http://arxiv.org/abs/2004.04173v4
- Date: Tue, 1 Feb 2022 07:24:09 GMT
- Title: Tensor network models of AdS/qCFT
- Authors: Alexander Jahn, Zolt\'an Zimbor\'as, Jens Eisert
- Abstract summary: We introduce the notion of a quasiperiodic conformal field theory (qCFT)
We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
- Score: 69.6561021616688
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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