Constructing a variational ground state of matter fermions coupled to a vison pair in Kitaev's honeycomb model

We develop a method to construct simple and explicit variational approximations for the ground state of Kitaev's honeycomb model with a nontrivial <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi mathvariant="double-struck">Z</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> flux configuration consisting of a pair of visons on neighboring plaquettes. The method consists of retaining only the largest singular values of the generator of the transformation between the vison pair and flux-free ground states. We compare physical quantities calculated using the approximate state to those obtained by extrapolating the results of exact diagonalization of finite lattices, finding them to be in very good agreement. We discuss ways to extend the method to more complicated flux configurations.