In:
Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 6 ( 2022-02-03), p. 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.
Type of Medium:
Online Resource
ISSN:
2521-327X
DOI:
10.22331/q-2022-02-03-643
Language:
English
Publisher:
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Publication Date:
2022
detail.hit.zdb_id:
2931392-2
Permalink
