Whitsitt, SethHenry, Louis-PaulSchuler, MichaelLäuchli, AndreasSachdev, Subir2019-10-092017-07-24Whitsitt, Seth, Michael Schuler, Louis-Paul Henry, Andreas M. Läuchli, and Subir Sachdev. 2017. Spectrum of the Wilson-Fisher Conformal Field Theory on the Torus. Physical Review B 96: 035142.2469-99502469-9969http://nrs.harvard.edu/urn-3:HUL.InstRepos:41505466We study the finite-size spectrum of the O(N)-symmetric Wilson-Fisher conformal field theory (CFT) on the (d=2)-spatial-dimension torus using the expansion in ε=3−d. This is done by deriving a set of universal effective Hamiltonians describing fluctuations of the zero-momentum modes. The effective Hamiltonians take the form of N-dimensional quantum anharmonic oscillators, which are shown to be strongly coupled at the critical point for small ε. The low-energy spectrum is solved numerically for N=1,2,3,4. Using exact diagonalization, we also numerically study explicit lattice models known to be in the O(2) and O(3) universality class, obtaining estimates of the low-lying critical spectrum. The analytic and numerical results show excellent agreement and the critical low-energy torus spectra are qualitatively different among the studied CFTs, identifying them as a useful fingerprint for detecting the universality class of a quantum critical point.en-USJournal Article2019-10-0910.1103/physrevb.96.035142