Sublattice scars and beyond in two-dimensional U(1) quantum link lattice gauge theories

In this article, we elucidate the structure and properties of a class of anomalous high-energy states of matter-free U(1) quantum link gauge theory Hamiltonians using numerical and analytical methods. Such anomalous states, known as quantum many-body scars in the literature, have generated a lot of interest due to their athermal nature. Our starting Hamiltonian is H=Okin+λOpot, where λ is a real-valued coupling, and Okin (Opot) are summed local diagonal (off-diagonal) operators in the electric flux basis acting on the elementary plaquette □. The spectrum of the model in its spin-12 representation on Lx×Ly lattices reveal the existence of sublattice scars, |ψs⟩, which satisfy Opot,□|ψs⟩=|ψs⟩ for all elementary plaquettes on one sublattice and Opot,□|ψs⟩=0 on the other, while being simultaneous zero modes or nonzero integer-valued eigenstates of Okin. We demonstrate a ``triangle relation'' connecting the sublattice scars with nonzero integer eigenvalues of Okin to particular sublattice scars with Okin=0 eigenvalues. A fraction of the sublattice scars have a simple description in terms of emergent short singlets, on which we place analytic bounds. We further construct a long-ranged parent Hamiltonian for which all sublattice scars in the null space of Okin become unique ground states and elucidate some of the properties of its spectrum. In particular, zero energy states of this parent Hamiltonian turn out to be exact scars of another U(1) quantum link model with a staggered short-ranged diagonal term.