  A novel algorithm based on the optimized decimation of tensor networks with
super-orthogonalization (ODTNS) that can be applied to simulate efficiently and
accurately not only the thermodynamic but also the ground state properties of
two-dimensional (2D) quantum lattice models is proposed. By transforming the 2D
quantum model into a three-dimensional (3D) closed tensor network (TN)
comprised of the tensor product density operator and a 3D brick-wall TN, the
free energy of the system can be calculated with the imaginary time evolution,
in which the network Tucker decomposition is suggested for the first time to
obtain the optimal lower-dimensional approximation on the bond space by
transforming the TN into a super-orthogonal form. The efficiency and accuracy
of this algorithm are testified, which are fairly comparable with the quantum
Monte Carlo calculations. Besides, the present ODTNS scheme can also be
applicable to the 2D frustrated quantum spin models with nice efficiency.
