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

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 |0rangle to Rydberg state |1rangle only when their closest neighbors are in |0rangle 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=|0cdots 0rangle. 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.