Establish Monte Carlo as a precision conformal spectrometer

Determine whether Monte Carlo simulations can be extended to high-precision measurements of multiple excited-state scaling dimensions in the one-dimensional long-range Ising model, thereby establishing Monte Carlo as a realistic conformal spectrometer.

Background

The generalized eigenvalue analysis used a basis of twenty local $\mathbb{Z}_2$-even operators and qualitatively isolated five different power laws. However, the extracted subleading exponents remained sensitive to fit windows and operator mixing. The paper therefore leaves unresolved whether larger operator bases, improved lattice representatives, and increased statistics can turn this exploratory spectroscopy into a controlled, high-precision determination of many operator dimensions and excited states.