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

Rath, Steffen Patrick and Simeth, Wolfgang and Endres, Manuel and Zwerger, Wilhelm (2013) Non-local order in Mott insulators, duality and Wilson loops. Annals of Physics, 334 . pp. 256-271. ISSN 0003-4916.

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It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local ‘parity order parameter’ which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [M. Endres, M. Cheneau, T. Fukuhara, C. Weitenberg, P. Schauß, C. Gross, L. Mazza, M.C. Bañuls, L. Pollet, I. Bloch, et al., Science 334 (2011) 200]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1) gauge theory in 2+1 dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.

Item Type:Article
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Endres, Manuel0000-0002-4461-224X
Additional Information:© 2013 Elsevier Inc. Received 11 February 2013. Accepted 4 April 2013. Available online 10 April 2013. We acknowledge useful comments by Nigel Cooper and Senthil Todadri. This work has been supported by the DFG Forschergruppe 801.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)Forschergruppe 801
Subject Keywords:Mott insulator; Optical lattice; Non-local order; Wilson loop; Duality
Record Number:CaltechAUTHORS:20160526-144821048
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Official Citation:Steffen Patrick Rath, Wolfgang Simeth, Manuel Endres, Wilhelm Zwerger, Non-local order in Mott insulators, duality and Wilson loops, Annals of Physics, Volume 334, July 2013, Pages 256-271, ISSN 0003-4916, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:67405
Deposited By: Ruth Sustaita
Deposited On:26 May 2016 22:00
Last Modified:30 Oct 2019 19:30

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