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.

71 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

References in corpus (9)

• Interacting anyons in topological quantum liquids: The golden chain
• Quantum circuits for strongly correlated quantum systems
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Rigorous free fermion entanglement renormalization from wavelet theory
• Scaling limits of lattice quantum fields by wavelets
• Rotational invariance in critical planar lattice models
• The action of the Virasoro algebra in quantum spin chains. I. The non-rational case
• Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach
• Quantum Simulation of Conformal Field Theory

Cited by in corpus (9)

• Scaling limits of lattice quantum fields by wavelets
• Convergence of Dynamics on Inductive Systems of Banach Spaces
• Variational quantum simulation of critical Ising model with symmetry averaging
• Chiral Virasoro algebra from a single wavefunction
• Multipartite Embezzlement of Entanglement
• Renormalisation of Quantum Cellular Automata
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Critical Fermions are Universal Embezzlers
• Holographic Tensor Networks as Tessellations of Geometry