Spectrum of the Wilson-Fisher conformal field theory on the torus

The authors study the finite-size energy spectrum of the O(N) symmetric Wilson-Fisher conformal field theory (CFT) on the spatial torus. They first perform an analytic calculation of the spectrum using the $ϵ$ expansion with a careful treatment of the zero-momentum modes. The authors also perform exact diagonalization on several lattice Hamiltonians whose critical points are known to be described by the Wilson-Fisher CFT. Comparison of the analytic and numerical data demonstrates that the energy spectrum is a useful diagnostic for determining the universality class of a critical point. These results have applications in determining the critical behavior of more complicated many-body systems.