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.

arXiv comment71 pages, 1 figure; further comparison with other approaches, clarified relation with Temperley-Lieb algebras, slightly expanded published version including comment on modified Koo-Saleur formula

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• Multipartite Embezzlement of Entanglement
• Renormalisation of Quantum Cellular Automata
• Critical Fermions are Universal Embezzlers
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Holographic Tensor Networks as Tessellations of Geometry