Symmetric Tensor Scars with Tunable Entanglement from Volume to Area Law

Teleportation of quantum information over long distances requires robust entanglement on the macroscopic scale. The construction of highly energetic eigenstates with tunable long-range entanglement can provide a new medium for information transmission. Using a symmetric superposition of the antipodal triplet states, we construct polynomially many exact zero-energy eigenstates for a class of nonintegrable spin-1/2 Hamiltonians with two-body interactions. These states exhibit nonthermal correlations, and hence, are genuine quantum many-body scars. By tuning the distribution of triplets, we induce extensive, logarithmic, or area-law entanglement and can observe a second-order entanglement phase transition. Quasiparticle excitations in this manifold converge to be exact quantum many-body scars in the thermodynamic limit. This framework has a natural extension to higher dimensions, where entangled states controlled by lattice geometry and internal symmetries can result in new classes of correlated out-of-equilibrium quantum matter. Our results provide a new avenue for entanglement control and quantum state constructions.