Yasaman Bahri, Ashvin Vishwanath
Topological phases which host Majorana fermions cannot be identified via local order parameters. We give simple non-local order parameters to distinguish quasi-1D topological superconductors of spinless fermions, for any interacting model in the absence of time reversal symmetry. These string or brane-type order parameters are amenable to measurements via quantum gas microscopy in cold atom systems, which could serve as an alternative route towards Majorana fermion detection that involves bulk rather than edge degrees of freedom. We also discuss our attempts at accessing 2D topological superconductors via the quasi-1D limit of coupling N identical chains with Z_{N} translation symmetry. We classify the resulting symmetric topological phases and discuss general rules for constructing non-local order parameters that distinguish them. The phases include quasi-1D analogs of (i) the p+ip topological superconductor, which can be distinguished up to the 2D Chern number mod 2, and (ii) the 2D weak topological superconductor. The non-local order parameters for some of these phases simply involve a product of the string order parameters for the individual chains. Finally, we sketch a physical picture of the topological phases as a condensate of Ising charged domain walls, which motivates the form of the non-local order parameter.
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http://arxiv.org/abs/1303.2600
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