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We show that Projected Entangled-Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number.
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Note however that in [ 15 ] it has been shown that expectation values of observables in chiral models can be expressed as a contraction of tensor networks, although the question whether states can be expressed as tensor networks was left open
Cited in the paper.
See Supplemental Material for an introduction on free fermionic systems and Chern insulators, a detailed explanation of the Gaussian formalism and GFPEPS, GFPEPS with particle number conservation, and how the Chern number can be extracted from such a GFPEPS
Cited in the paper.
Note that this construction does not work in 1D if the number of Majorana bonds is odd, such as for the Kitaev chain [ 26 ]
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