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arXiv:1302.0693 · Annals of Physics

Non-local order in Mott insulators, duality and Wilson loops

Steffen Patrick Rath, Wolfgang Simeth, Manuel Endres, W. Zwerger

Published Apr 26, 2013• 25 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2013.04.006

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This paper reviews a recent non-Landau-Ginzburg-Wilson (LGW) approach to superfluid to Mott insulator transitions in two dimensional bosonic lattice systems, using a dual vortex field theory [L. Balents, L. Bartosch, A. Burkov, S. Sachdev and K. Sengupta, Phys. Rev. B 71 (2005), 144508; Phys. Rev. B 71 (2005), 144509]. The physical interpretation of conventional LGW theory of quantum criticality is re-examined and similarities and differences with the vortex picture are discussed. The “unification” of various competing (insulating) orders, and the coincidence of these orders with the Mott transition are readily understood formulation. Some aspects of the recent theory of “deconfined” quantum criticality, which are to an extent subsumed approach, are discussed. A pedagogical presentation of the “nuts and bolts” of boson-vortex duality at the hamiltonian level is included, tailored to a condensed matter audience.
In the t-J model, the electron fractionalization is dictated by the phase string effect. We find that in the underdoped regime, the antiferromagnetic and superconducting phases are dual: in the former, holons are confined while spinons are deconfined, and vice versa in the latter. These two phases are separated by a novel phase, the so-called Bose-insulating phase, where both holons and spinons are deconfined. A pair of Wilson loops was found to constitute a complete set of order parameters determining this zero-temperature phase diagram. The quantum phase transitions between these phases are suggested to be of non-Landau-Ginzburg-Wilson type.