Symmetric tensor scars with tunable entanglement from volume to area law

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.

Figures (6)

• Figure 1: (a) A symmetric tensor state for $N=3$, a zero-energy eigenstate of \ref{['eq:SH']}. Each component is a tensor product of three triplet types ($T_1$, $T_2$, $T_3$) between antipodal sites. (b) Phase diagram for the Bell basis states. Colour indicates the half-system entropy $S^{(2)}$ for $N{=}4001$. White lines indicate the boundary between volume-scaling entanglement (V) and log-scaling entanglement phases (L). The red dashed line indicates $k_x {=} k_y$ which is shown in more detail in panels (c-e), wherein increasing saturation indicates increasing $N$ from 201 to 4001, in steps of 200. Along this line, we show entanglement rescaled by (c) $\ln N$ and (d) $N$ to demonstrate the two scalings. (e) Susceptability $\chi = (1/N)\mathrm{d}^2 S^{(2)} / \mathrm{d} k_z^2$ exhibits a crossing evidencing a second-order phase transition.
• Figure 2: Entanglement for the symmetric tensor states in the conventional basis. (a) $S^{(2)}$ vs subsystem size $l$ for all states with $N=9$. The color denotes $\langle S^2_{\text{tot}}\rangle$ of the corresponding state. Example states showcasing the (b) area-law, (c) log-law, and (d) volume-law entanglement scaling of half-chain entropy. Lines in (c) are fits to $a\ln N+b$.
• Figure S1: Behavior of von-Neumann entanglement entropy for different cuts for (a) Bell and (b) Conventional basis. The system size is $2N=18$.
• Figure S2: Von Neumann entanglement entropy ($S^{\text{vN}}$) as a function of subsystem size ($l$) for the symmetric tensor states in (a) Bell and (b) conventional basis. The system size is $2N=18$.
• Figure S3: Stability of STS under $P_1$: Behavior of overlaps $O(E')$ and the dynamics of Fidelity ($F(t)$) and structure factor ($S_{\pi}(t)$) from the initial states $(5,0,2)$ (in panel (a),(b)), $(1,1,5)$ (in panel (c), (d)), $(3,3,1)$ (in panel (e), (f)). $L=2N=14$, $h_z=0.2$.