Conformal Field Theory from Lattice Fermions

verfasst von: Tobias J. Osborne, Alexander Stottmeister
Abstract: We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions, focussing on free fermion models and Wess-Zumino-Witten models. To this end, we utilize a recently introduced operator-algebraic framework for Wilson-Kadanoff renormalization. In this setting, we prove the convergence of the approximation of the Virasoro generators by the Koo-Saleur formula. From this, we deduce the convergence of lattice approximations of conformal correlation functions to their continuum limit. In addition, we show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
Organisationseinheit(en): Institut für Theoretische Physik
QuantumFrontiers
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)
Typ: Artikel
Journal: Communications in Mathematical Physics
Band: 398
Seiten: 219-289
Anzahl der Seiten: 71
ISSN: 0010-3616
Publikationsdatum: 02.2023
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Statistische und nichtlineare Physik, Mathematische Physik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2107.13834 (Zugang: Offen)
https://doi.org/10.1007/s00220-022-04521-8 (Zugang: Offen)

BibTeX

@article{10a4b43b7b08453cb712b461f0715db0,
title = "Conformal Field Theory from Lattice Fermions",
abstract = " We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions, focussing on free fermion models and Wess-Zumino-Witten models. To this end, we utilize a recently introduced operator-algebraic framework for Wilson-Kadanoff renormalization. In this setting, we prove the convergence of the approximation of the Virasoro generators by the Koo-Saleur formula. From this, we deduce the convergence of lattice approximations of conformal correlation functions to their continuum limit. In addition, we show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories. ",
keywords = "math-ph, hep-th, math.MP, math.OA, quant-ph, 81T17, 81T05, 81T25, 81T27, 81-10, 42C40",
author = "Osborne, {Tobias J.} and Alexander Stottmeister",
note = "Funding Information: The authors would like to thank R. F. Werner for valuable discussion about inductive limits in quantum theory. AS would like to thank Y. Tanimoto for helpful discussions concerning the essential self-adjointness of smeared Virasoro generators. Moreover, the authors would like to extend their gratitude to the unknown reviewers providing valuable feedback on a previous version of the manuscript, which improved the presentation and clarified the relation to existing work. Special thanks are extended to one of the reviewers for suggesting to clarify the relation with the Temperley-Lieb algebra and suggesting the case of symplectic fermions for future work. This work was supported, in part, by the DFG through SFB 1227 (DQ-mat), Quantum Valley Lower Saxony, and funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy EXC-2123 QuantumFrontiers 390837967.",
year = "2023",
month = feb,
doi = "10.48550/arXiv.2107.13834",
language = "English",
volume = "398",
pages = "219--289",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",
}