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)