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

Spectrum of the Wilson-Fisher conformal field theory on the torus 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=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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

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

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

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=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.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.035142
Publisher site
See Article on Publisher Site

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=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.

Journal

Physical Review BAmerican Physical Society (APS)

Published: Jul 24, 2017

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