Emergent SU(2) Dynamics and Perfect Quantum Many-Body Scars

Motivated by recent experimental observations of coherent many-body revivals in a constrained Rydberg atom chain, we construct a weak quasilocal deformation of the Rydberg-blockaded Hamiltonian, which makes the revivals virtually perfect. Our analysis suggests the existence of an underlying nonintegrable Hamiltonian which supports an emergent SU(2)-spin dynamics within a small subspace of the many-body Hilbert space. We show that such perfect dynamics necessitates the existence of atypical, nonergodic energy eigenstates—quantum many-body scars. Furthermore, using these insights, we construct a toy model that hosts exact quantum many-body scars, providing an intuitive explanation of their origin. Our results offer specific routes to enhancing coherent many-body revivals and provide a step toward establishing the stability of quantum many-body scars in the thermodynamic limit.

Figure 1

Nonthermalizing dynamics in constrained spin Hamiltonians. (a) Many-body fidelity $g(t)$ as a function of time for the Hamiltonian $H_0$ without any perturbations and with optimal perturbations Eqs. (3) and (4). The inset shows the infidelity, $1-g(t)$. (b) Half-chain bipartite entanglement entropy (EE) dynamics. At the optimal perturbation point, the EE shows bounded, oscillatory dynamics. The inset shows the eigenvalues $p_{\mu }(t)$ of the half-chain reduced density matrix. Numerical simulations are performed with $N=32$ starting from the Néel state. (c) Optimized perturbation strengths $h_d$ decay exponentially. Solid line indicates the analytical ansatz function (4).

Figure 2

(a) The overlap of $|{\mathbb{Z}}_2⟩$ with energy eigenstates of $H$ is dominated by $N+1$ special ones (red circles), well separated from the bulk. The density of data points is color coded. (b) Eigenvalue level statistics of both $H_0$ and $H$ for $N=32$ closely follow that of Wigner-Dyson class of the Gaussian orthogonal ensemble. (c) Level statistics indicator $⟨r_i⟩$ as a function of system size $N$ flows to its value in the Wigner-Dyson ensemble, indicating that the bulk of the system remains ergodic. All data is for the momentum $k=0$, inversion even sector.

Figure 3

Emergent SU(2) structure in the subspace $\mathcal{K}$. (a) Matrix elements of the operator $H^{+}$ between consecutive vectors $|k⟩$ are in excellent agreement with that of an appropriately rescaled raising operator $S^{+}$ in the $s=N/2$ representation of the su(2) algebra shown as the solid curve. (b) The FSA basis vectors $|k⟩$ are approximate eigenstates of the operator $H^z$ with harmonically spaced eigenvalues. The inset shows the residual of the eigenvalue spacing ${\mathrm{\Delta }}_k\equiv H_{k+1}^z-H_k^z$ away from its mean value. The error bars are extracted from variances in the expectation values of $H^z$ in $|k⟩$.