Beyond mean field theory: a way from braids and knots to quantum dimers

Alexander Protogenov

Russian Academy of Sciences, Institute of Applied Physics, Nizhny Novgorod, Russian Federation

We consider inhomogeneous current states in both framework of two-component Ginzburg-Landau model and in 2D lattice. We demonstrate also the mapping of toroid current states into quantum dimer states of the exact solvable Roksar-Kivelson-like model.

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