Emergent photons and transitions in the O(3) sigma model with hedgehog suppression

By O. Motrunich, Ashvin Vishwanath. 2003

177 citations recorded by the source corpus.

We study the effect of hedgehog suppression in the O(3) sigma model in D = 2 + 1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting paramagnetic state has gauge charged matter with half-integer spin (spinons) and also an emergent gauge field (photons), whose existence is explicitly demonstrated. Hence, this is an explicit realization of fractionalization in a model with global SU(2) symmetry. The zero-temperature ordering transition from this phase is found to be continuous but distinct from the regular Heisenberg ordering transition. We propose that these phases and this phase transition are captured by the noncompact CP1 model, which contains a pair of bosonic fields coupled to a noncompact U(1) gauge field. Direct simulation of the transition in this model yields critical exponents that support this claim. The easy-plane limit of this model also displays a continuous zero temperature ordering transition, which has the remarkable property of being self-dual. The presence of emergent gauge charge and hence Coulomb interactions is evidenced by the presence of a finite temperature Kosterlitz-Thouless transition associated with the thermal ionization of the gauge charged spinons. Generalization to higher dimensions and the effects of nonzero hedgehog fugacity are discussed.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/84f7c6cf38edf5e768daed4da20d228fb15e4bf8

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Citations in the corpus

Deconfined quantum critical points: symmetries and dualities (2017, background): “The easy-plane theory is known to be self-dual [53], in the sense that it is dual to another easy-plane NCCP(1) theory,”
Particle-Vortex Duality from 3D Bosonization (2016, background): “We have the self-duality ZQED[Ns=2][A;C] = Z̄QED[Ns=2][−2C;− 1 2 A] This duality was previously studied in [58].”
Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect (2012, background): “(10) closely resembles the action for a deconfined quantum critical point (noncompact CP1 theory with easy-plane anisotropy) [20,41].”
Holographic Quantum Matter (2016, background): “In some cases, such as non-compact CP(1) models [562] or supersymmetric QED3 [434], the theory is mapped back to iteslf by the particle-vortex transformation.”
Holographic Quantum Critical Transport without Self-Duality (2010, background): “a single complex scalar, as we reviewed in section 6.1: note that this theory is not self-dual (and selfduality is not expected in general, except for a particular theory with two complex scalar elds [7, 42]). In the single scalar eld case, as discussed in section 6.1, KT;L characterize the transver”
Quantum critical transport, duality, and M-theory (2007, methodology): “On the other hand, unlike these other examples, the universal relation (4.1) applies at arbitrary ω and k. Acknowledgments We thank M. Ernebjerg, J. Liu, D. Shih, M. Strassler, A. Strominger, C. Vafa, and A. Vishwanath for useful discussions.”
Spin Ice, Fractionalization, and Topological Order (2011, background): “B 74:024302–12 [75] Motrunich OI, Vishwanath A.”
Quantum magnetism and criticality (2007, background): “Let us assume that Sz remains a valid description across a quantum phase transition at s = sc, and ask about the nature of the quantum state [24] for s > sc.”