Scars from protected zero modes and beyond in U (1) quantum link and quantum dimer models

We demonstrate the presence of anomalous high-energy eigenstates, or many-body scars, in U (1) quantum link and quantum dimer models on square and rectangular lattices. In particular, we consider the paradigmatic Rokhsar-Kivelson Hamiltonian H = O-kin + lambda O-pot where O-pot (O-kin) is defined as a sum of terms on elementary plaquettes that are diagonal (off-diagonal) in the computational basis. Both these interacting models possess an exponentially large number of mid-spectrum zero modes in system size at lambda = 0 that are protected by an index theorem preventing any mixing with the nonzero modes at this coupling. We classify different types of scars for vertical bar lambda vertical bar less than or similar to O(1) both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys. Rev. Lett. 126, 220601 (2021)]. The scars at finite lambda show a rich variety with those that are composed solely from the zero modes of O-kin, those that contain an admixture of both the zero and the nonzero modes of O-kin, and finally those composed solely from the nonzero modes of O-kin. These scars have tell-tale energies such as (non-zero) integers and irrationals like +/-root 2 at lambda = 0 or n(1)lambda +/- n(2) at lambda not equal 0 where both n(1), n(2) are integers. We give analytic expressions for certain "lego scars" for the quantum dimer model on rectangular lattices where one of the linear dimensions can be made arbitrarily large, with the building blocks (legos) being composed of emergent singlets and other more complicated entangled structures. Published by the SciPost Foundation.