Spectrum of the Wilson-Fisher Conformal Field Theory on the Torus
Fig. 10. Finite-size critical low-energy spectrum for the Spin-1 O(2) model Eq. on a square lattice.*
Harvard Physics grad student Seth Whitsitt, Prof. Subir Sachdev, and colleagues from Universität Innsbruck, recently published their study of the finite-size energy spectrum of the O(N) symmetric Wilson-Fisher conformal field theory (CFT) on the spatial torus. In the study, the physicists first perform an analytic calculation of the spectrum using the expansion with a careful treatment of the zero-momentum modes. Then they also performed exact diagonalization on several lattice Hamiltonians whose critical points are known to be described by the Wilson-Fisher CFT. After comparing the analytic and numerical data, the authors concluded 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.
*See Seth Whitsitt, Michael Schuler, Louis-Paul Henry, Andreas M. Läuchli, and Subir Sachdev, "Spectrum of the Wilson-Fisher Conformal Field Theory on the Torus," Physical Reveiw B (2017) DOI: https://doi.org/10.1103/PhysRevB.96.035142.