  In the tensor-network framework, the expectation values of two-dimensional
quantum states are evaluated by contracting a double-layer tensor network
constructed from initial and final tensor-network states. The computational
cost of carrying out this contraction is generally very high, which limits the
largest bond dimension of tensor-network states that can be accurately studied
to a relatively small value. We propose an optimized contraction scheme to
solve this problem by mapping the double-layer tensor network onto an
intersected single-layer tensor network. This reduces greatly the bond
dimensions of local tensors to be contracted and improves dramatically the
efficiency and accuracy of the evaluation of expectation values of
tensor-network states. It almost doubles the largest bond dimension of
tensor-network states whose physical properties can be efficiently and reliably
calculated, and it extends significantly the application scope of
tensor-network methods.
