Conformal fields and operator product expansion in critical quantum spin chains

Abstract: We propose a variational method for identifying lattice operators in a critical quantum spin chain with scaling operators in the underlying conformal field theory (CFT). In particular, this allows us to build a lattice version of the primary operators of the CFT, from which we can numerically estimate the operator product expansion coefficients $C_{\alpha\beta\gamma}^{\textrm{ CFT}}$. We demonstrate the approach with the critical Ising quantum spin chain.