Generalized Spin Helix States as Quantum Many-Body Scars in Partially Integrable Models

Abstract

Quantum many-body scars are highly excited eigenstates of non-integrable Hamiltonians which violate the eigenstate thermalization hypothesis and are embedded in a sea of thermal eigenstates. We provide a general mechanism to construct partially integrable models with arbitrarily large local Hilbert space dimensions, which host exact many-body scars. We introduce designed integrability-breaking terms to several exactly solvable spin chains, whose integrable Hamiltonians are composed of the generators of the Temperley-Lieb algebra. In the non-integrable subspace of these models, we identify a special kind of product states -- the generalized spin helix states as exact quantum many-body scars, which lie in the common null space of the non-Hermitian generators of the Temperley-Lieb algebra and are annihilated by the integrability-breaking terms. Our constructions establish an intriguing connection between integrability and quantum many-body scars, meanwhile provide a systematic understanding of scarred Hamiltonians from the perspective of non-Hermitian projectors.

Figures (2)

• Figure 1: (a) Generalized spin helix states for higher-spin models. The spin vectors (the black arrows) of the higher spins (the colorful spheres) wind in the $S^x–S^y$ plane, while maintaining a fixed angle with the $S^z$ axis. (b) A pictorial illustration for the partially integrable Hamiltonian Eq. \ref{['eq:perturbed']} hosting the generalized spin helix states as exact quantum many-body scars. The local degrees of freedom on each site are divided into two sets $A$ and $B$. The interactions between the basis states in $A$ and those in $B$ constitute the XXC Hamiltonian, while the interactions between different basis states within $A$ or $B$ take the form of $Ph'P$ (see the main text).
• Figure 2: (a) Level spacing statistics of the non-integrable subspace of the $N=3$ partially integrable model. (b) Bipartite entanglement entropy of the thermal eigenstates (gray dots) and scarred eigenstates (red diamonds) within the non-integrable subspace, as a function of the eigenenergy and the expectation value of total $S^z$. $L=9$, $\gamma=2\pi/9$, other parameters taken as the same as those in (a).