Symmetric tensor scars with tunable entanglement from volume to area law

TL;DR

The paper constructs exact zero-energy eigenstates with tunable entanglement in non-integrable spin systems, revealing a second-order entanglement phase transition and extending to higher dimensions for novel quantum matter.

Contribution

It introduces a method to generate quantum many-body scars with controllable entanglement, including volume and area-law regimes, in non-integrable spin Hamiltonians.

Findings

States exhibit non-thermal correlations as genuine quantum scars.

Tunable entanglement induces a phase transition from volume to area law.

Framework extends to higher dimensions for new quantum phases.

Abstract

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 non-integrable spin-1/2 Hamiltonians with two-body interactions. These states exhibit non-thermal correlations, 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.