Topological order and conformal quantum critical points

Eddy Ardonne, Paul Fendley, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


We discuss a certain class of two-dimensional quantum systems which exhibit conventional order and topological order, as well as quantum critical points separating these phases. All of the ground-state equal-time correlators of these theories are equal to correlation functions of a local two-dimensional classical model. The critical points therefore exhibit a time-independent form of conformal invariance. These theories characterize the universality classes of two-dimensional quantum dimer models and of quantum generalizations of the eight-vertex model, as well as ℤ2 and non-abelian gauge theories. The conformal quantum critical points are relatives of the Lifshitz points of three-dimensional anisotropic classical systems such as smectic liquid crystals. In particular, the ground-state wave functional of these quantum Lifshitz points is just the statistical (Gibbs) weight of the ordinary two-dimensional free boson, the two-dimensional Gaussian model. The full phase diagram for the quantum eight-vertex model exhibits quantum critical lines with continuously varying critical exponents separating phases with long-range order from a ℤ2 deconfined topologically ordered liquid phase. We show how similar ideas also apply to a well-known field theory with non-Abelian symmetry, the strong-coupling limit of 2 + 1-dimensional Yang-Mills gauge theory with a Chern-Simons term. The ground state of this theory is relevant for recent theories of topological quantum computation.

Original languageEnglish (US)
Pages (from-to)493-551
Number of pages59
JournalAnnals of Physics
Issue number2
StatePublished - Apr 2004
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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