Disentangling Multiple Scaling Dimensions via Operator Covariance in Critical Quantum Spin Systems

Abstract

We present a general proof of different power-law decays versus distance of the eigenvalues of two-point covariance matrices in critical lattice quantum models, allowing extraction of multiple scaling dimensions. We demonstrate the practical utility of this method in the context of a spin-1/2 chain with critical ground state described by the SU(2)_1 Wess–Zumino–Witten field theory. Using quantum Monte Carlo simulations to compute covariance matrices in different symmetry sectors, we resolve the expected relevant and marginal primary operators as well as some descendants. The covariance method can be integrated into many existing numerical schemes and promises to significantly enhance computational studies of quantum criticality.