Conformal Field Theory from Lattice Fermions

authored by: 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.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
Type: Article
Journal: Communications in Mathematical Physics
Volume: 398
Pages: 219-289
No. of pages: 71
ISSN: 0010-3616
Publication date: 02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Mathematical Physics
Electronic version(s): https://doi.org/10.48550/arXiv.2107.13834 (Access: Open)
https://doi.org/10.1007/s00220-022-04521-8 (Access: Open)

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",
}