Towers of Quantum Many-body Scars from Integrable Boundary States

We construct several models with multiple quantum many-body scars (QMBS) using integrable boundary states (IBS). Specifically, we focus on the tilted Néel states, which are parametrized IBS for the spin-1/2 Heisenberg chain, and show that these states can be used to construct a tower of scar states. Our models exhibit periodic revival dynamics, showcasing a characteristic behavior of superpositions of QMBS. Furthermore, the tower of QMBS found in this study possesses a restricted spectrum generating algebra (RSGA) structure, indicating that QMBS are equally spaced in energy. This approach can be extended to two-dimensional models, which can be decomposed into an array of one-dimensional models. In this case, the tilted Néel states again serve as parent states for multiple scar states. These states demonstrate low entanglement entropy, marking them as exact scar states. Notably, their entanglement entropy adheres to the sub-volume law, further solidifying the nonthermal properties of QMBS. Our results provide novel insights into constructing QMBS using IBS, thereby illuminating the connection between QMBS and integrable models.

💡 Research Summary

In this work the authors develop a systematic construction of multiple quantum many‑body scar (QMBS) states by exploiting integrable boundary states (IBS). The starting point is the family of tilted Néel states, which are known to be IBS of the spin‑½ Heisenberg chain. These states are annihilated by all odd‑order conserved charges Q₂k+1 of the integrable model, in particular by the third conserved charge C_SC (the scalar spin chirality).

The authors first introduce a non‑integrable Hamiltonian
H₁(g, h_y)=C_SC + g H_pert + h_y Y,
where H_pert is a sum of two‑site projectors that also annihilate the tilted Néel states, and Y is the total spin‑y component providing a U(1) symmetry. Because the tilt parameter α is arbitrary, the tilted Néel states can be projected onto eigenstates of Y with definite magnetization. This yields a tower of exact eigenstates |Ψ_n⟩ (n=0,…,L) with energies E_n=(L−2n)h_y, i.e. equally spaced levels. The level‑spacing statistics of H₁ follow the GUE distribution, confirming its non‑integrability, while the half‑chain entanglement entropy of |Ψ_n⟩ scales as (1/2) ln L, a sub‑volume law that signals strong ETH violation.

A restricted spectrum‑generating algebra (RSGA) of order two underlies this tower. The reference state |Ψ_0⟩, the Hamiltonian H₁, and the lowering operator O_{−π} satisfy four algebraic relations: (i) H₁|Ψ_0⟩=L h_y|Ψ_0⟩, (ii)