Speaker
Description
The PXP chain is the standard example of weak ergodicity breaking: a Neel product state fails to thermalise, returning periodically for long times, and the return is attributed to a tower of nearly equally spaced eigenstates. How nearly equally spaced they are, and whether the resulting revivals survive in the thermodynamic limit, has not been settled. We solve the forward-scattering approximation, the standard analytic model of that tower, exactly. The hopping amplitudes of the forward-scattering chain, previously available only numerically, are obtained in closed form, and their deviation from a perfect SU(2) multiplet is computed analytically in the thermodynamic limit. It converges to a fixed profile rather than vanishing, so the tower is not an SU(2) multiplet at any system size. This does not, however, spoil the revivals. The Neel state occupies only a narrow central window of the tower, where the level spacings are uniform to order 1/L, and the revival fidelity within the forward-scattering subspace approaches unity as the chain grows. Since the true PXP revivals decay with system size, the anharmonicity of the tower cannot be what limits scarring.