The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians.Our model is based on the PXP-type interactions without disorder.We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions.This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis.Through the exact expression of the scar states, the underlying physical mechanism is clarified.Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.
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⟩ to Rydberg state
∣1⟩ only when their closest neighbors are in
∣0⟩ 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
∣0⟩=∣0⋯0⟩. 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.