# Conformal fields and operator product expansion in critical quantum spin chains

## TL;DR

This paper introduces a variational method to identify lattice operators with conformal field theory operators in critical quantum spin chains, enabling numerical estimation of OPE coefficients, demonstrated on the critical Ising model.

## Contribution

A novel variational approach to map lattice operators to CFT operators and compute OPE coefficients in critical quantum spin chains.

## Key findings

- Successfully identified lattice primary operators in the critical Ising chain.
- Numerically estimated the OPE coefficients matching CFT predictions.
- Provided a practical method for connecting lattice models with conformal field theories.

## 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.