Exact tensor network representations for a frustrated spin system at large finite S

The tensor network approach has been shown to be a powerful tool to study entanglement of frustrated spin systems. Nevertheless, it usually requires high computational capability even for spin-half case, e.g. the kagome lattice. Counterintuitively, we expect that in the semiclassical regime (large spin S case), the representation of a wavefunction could be found without high computational requirement. We study the phase diagram of the frustrated spin ladder model and find a highly frustrated point in the classical limit at which all the eigenstates at finite spin S that approach the ground state as S goes to infinity are identified. At spin S these states are the rung singlet states and the set of Haldane states of spin 1 to spin 2S. All these states can be represented by tensor networks. Studies in the semiclassical regime, in general, give a clue of the phase in the quantum regime, and thus point a direction to search for novel quantum phases in future numerical works.