Nonthermal Dynamics of a One-dimensional Rydberg-atom Chain with Constraint Four-body Interactions

Abstract

We investigate dynamics of a linear chain of Rydberg atoms driven by a constrained four-body interaction, where two neighboring atoms are excited simultaneously from the electronic ground state $|0\rangle$ to Rydberg state $|1\rangle$ only when their closest neighbors are in $|0\rangle$ state. By employing an ansatz for the many-body ground state, the low-energy Hamiltonian is given by a tridiagonal form. The many-body ground state energy, which scales linearly with the chain length $L$, is obtained analytically in the thermodynamic limit and agrees with the one of the exact diagonalization. Our model supports quantum many-body scar eigenstates that are nearly equally spaced energetically. The scar states overlap strongly with the basis state $|\mathbf{0}\rangle=|0\cdots 0\rangle$. We show that the overlap distribution is tilted by the state-dependent four-body interaction. This leads to non-ergodic dynamics, evidenced by the revival of the initial state. The four-body constrained model can be realized with Rydberg atoms in a Peierls array with alternating bond lengths, where atoms on the shorter and longer bonds experience Rydberg blockade and antiblockade, respectively. Our study provides a pathway to explore constrained non-ergodic dynamics with four-body interactions by combining the Rydberg blockade and antiblockade.