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

Understand

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 $H=\mathcal{O}_{\mathrm{kin}} + \lambda \mathcal{O}_{\mathrm{pot}}$ where $\mathcal{O}_{\mathrm{pot}}$ ($\mathcal{O}_{\mathrm{kin}}$) 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 $|\lambda| \lesssim \mathcal{O}(1)$ both at zero and finite winding number sectors complementing and significantly generalizing our previous work [Banerjee and Sen, Phys.