Quantum scars from zero modes in an Abelian lattice gauge theory on ladders

We consider the spectrum of a U(1) quantum link model where gauge fields are realized as S=1/2 spins and demonstrate a new mechanism for generating quantum many-body scars (high-energy eigenstates that violate the eigenstate thermalization hypothesis) in a constrained Hilbert space. Many-body dynamics with local constraints has attracted much attention due to the recent discovery of non-ergodic behavior in quantum simulators based on Rydberg atoms. Lattice gauge theories provide natural examples of constrained systems since physical states must be gauge-invariant. In our case, the Hamiltonian H={cal O}_{rm kin}+λ{cal O}_{rm pot}, where {cal O}_{rm pot} ${cal O}_{rm kin}$ is diagonal (off-diagonal) in the electric flux basis, contains exact mid-spectrum zero modes at λ=0 whose number grows exponentially with system size. This massive degeneracy is lifted at any non-zero λ but some special linear combinations that simultaneously diagonalize {cal O}_{rm kin} and {cal O}_{rm pot} survive as quantum many-body scars, suggesting an "order-by-disorder" mechanism in the Hilbert space. We give evidence for such scars and show their dynamical consequences on two-leg ladders with up to 56 spins, which may be tested using available proposals of quantum simulators. Results on wider ladders point towards their presence in two dimensions as well.