Topological Order and Conformal Quantum Critical Points

By E. Ardonne, P. Fendley, E. Fradkin. 2003

327 citations recorded by the source corpus.

Abstract 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 Z 2 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 Z 2 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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/d1727d3bb2ef377a94987c8021d9b78945a91d47

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Membranes at Quantum Criticality (2008, background): “This is a hallmark of similar constructions in nonequilibrium dynamics [22], dynamical critical phenomena [23, 24], quantum critical systems [9, 25] and stochastic quantization [26–28].”
An analytic Lifshitz black hole (2009, background): “] = Z ddxdt h (∂tχ) 2 − K ∇2χ 2i (1.1) This action describes a ﬁxed line parametrized by K, and the dynamical exponent is z= 2. This theory describes the critical behavior of e.g.quantum dimer models [3]. In many ways, the d= 2,z= 2 version of the theory (1.1) is like a relativistic boson in 1+1 dim”
Quantum Criticality Under Decoherence or Weak Measurement (2023, methodology): “The ground state wave function can be derived for gapped states such as SPT phases [9, 16, 17], and also gapless phases with a Gaussian (free boson) Lagrangian, such as the (1 + 1)d Luttinger liquid [1], or the Rokhsar-Kivelson (RK) point in (2+1)d models [32].”
Lifshitz spacetimes from AdS null and cosmological solutions (2010, methodology): “[31], representing universality classes of dimer statistical systems [32], or as representing certain phases of systems with antiferromagnetic interactions as well as in models of liquid crystals [33].”