Conformal field theory from lattice fermions

TL;DR

This paper establishes a rigorous method for approximating 1+1-dimensional conformal field theories using lattice fermions, proving convergence of key operators and correlation functions, and providing error estimates for quantum simulations.

Contribution

It introduces a lattice approximation framework for conformal field theories using operator-algebraic methods, demonstrating convergence and error bounds.

Findings

Proves convergence of Virasoro generators via Koo-Saleur formula.

Shows lattice correlation functions converge to continuum limits.

Provides explicit error estimates for quantum simulation accuracy.

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.