Multiple Scaling Dimensions from Operator Covariance in Monte Carlo Simulations

Learn a novel computational method for extracting multiple scaling dimensions from Monte Carlo simulations of critical systems through operator covariance matrix diagonalization. Explore how this technique efficiently computes scaling dimensions beyond the standard critical exponents by leveraging eigenvalue analysis in regimes exhibiting power-law decays. Examine practical applications of this approach through detailed case studies including 2D and 3D classical Ising models, the Blume-Capel model at its tricritical point, and 1D quantum systems. Discover how this methodology extends beyond traditional Hamiltonian spectrum extraction to disentangle scaling dimensions in critical phenomena. Investigate the potential applications of this technique for studying complex multi-critical points, particularly the SO(5) "deconfined" multi-critical point in J-Q model settings, providing new tools for understanding critical behavior in statistical mechanics and quantum many-body systems.