Abstract
We study the finite-size spectrum of the O()-symmetric Wilson-Fisher conformal field theory (CFT) on the ()-spatial-dimension torus using the expansion in . 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 -dimensional quantum anharmonic oscillators, which are shown to be strongly coupled at the critical point for small . The low-energy spectrum is solved numerically for . 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.
3 More- Received 26 March 2017
DOI:https://doi.org/10.1103/PhysRevB.96.035142
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