Discrete sliding symmetries, dualities, and self-dualities of quantum orbital compass models and p+ip superconducting arrays

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 19, 2005, Pages

  Nussinov, Zohar ^a,b   Fradkin, Eduardo ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b WASHINGTON UNIVERSITY   (United States)

^c University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33344454409     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.195120     Document Type: Article

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46. In this paper, a self-duality (derived via a Poisson summation formula route to dualities), was found for several classical ZN and U (1) models. The self-dualities of Amit invert a two-site term [analogous to the two field term in the Euclidean rendition of the transverse magnetic field term of Eq. 6] with a higher order multiple site term [analogous to the forms borne by the plaquette term in Eq. 6]. Similar to Refs. and, in the work of Amit, it was found that the self-dualities in such models invert the magnitudes of the different coupling constants. That is to say, the self-duality in these models relates the magnitude of the two site terms in the original variables to the magnitudes of the higher order multisite terms in the dual variables (and vice versa). In the current publication, we illustrate why, in certain instances, such an inversion among different terms is, by simple geometrical grounds, often anticipated. In particular, we explicitly illustrate why such relations are natural for the Xu-Moore model of Eq. 6.
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