A. B. Kuklov, A. M. Tsvelik
We study a quantum phase transition in a system of dipoles confined in a stack of $N$ identical one-dimensional ("cigar"-type) layers and polarized perpendicularly to the layers. In this arrangement the intra-layer interaction is purely repulsive preventing the system collapse and the inter-layer one is attractive. The dipoles may represent polar molecules confined in the optical lattice or indirect excitons in multi-layered structures. The transition separates two phases; in one of them superfluidity (understood as algebraic decay of the corresponding correlation functions) takes place on each individual layer, in the other the order parameter is the product of bosonic operators of all layers. We argue that in the presence of finite inter-layer tunneling the transition belongs to the universality class of the $q=N$ two-dimensional classical Potts model. For $N=2,3,4$ the corresponding low energy field theory is the model of Z$_N$ parafermions perturbed by the thermal operator. Results of Monte Carlo simulations are consistent with these predictions. The detection scheme of the chain superfluid is outlined.
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http://arxiv.org/abs/1207.4986
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