Variational tensor network operator

We propose a simple and generic construction of the variational tensor network operators to study quantum spin systems by synergy ideas from imaginary-time evolution optimization trial wave functions. By applying these initial states, accurate ground-state functions with extremely few parameters can be obtained. Furthermore, framework applied spontaneously symmetry-breaking, symmetry-protected topological, intrinsic topologically ordered phases, we show that symmetries local tensors associated phases emerge directly after without any gauge fixing. This provides universal way identify phase transitions prior knowledge system.