• Editors' Suggestion

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

Seth Whitsitt, Michael Schuler, Louis-Paul Henry, Andreas M. Läuchli, and Subir Sachdev
Phys. Rev. B 96, 035142 – Published 24 July 2017

Abstract

We 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=3d. 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 26 March 2017

DOI:https://doi.org/10.1103/PhysRevB.96.035142

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Seth Whitsitt1, Michael Schuler2, Louis-Paul Henry2, Andreas M. Läuchli2, and Subir Sachdev1,3

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
  • 3Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 96, Iss. 3 — 15 July 2017

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×