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We consider the spectrum of a $U(1)$ quantum link model where gauge fieldsare realized as $S=1/2$ spins and demonstrate a new mechanism for generatingquantum many-body scars (high-energy eigenstates that violate the eigenstatethermalization hypothesis) in a constrained Hilbert space. Many-body dynamicswith local constraints has attracted much attention due to the recent discoveryof non-ergodic behavior in quantum simulators based on Rydberg atoms. Latticegauge theories provide natural examples of constrained systems since physicalstates must be gauge-invariant. In our case, the Hamiltonian $H={\cal O}_{\rmkin}+\lambda {\cal O}_{\rm pot}$, where ${\cal O}_{\rm pot}$ (${\cal O}_{\rmkin}$) is diagonal (off-diagonal) in the electric flux basis, contains exactmid-spectrum zero modes at $\lambda=0$ whose number grows exponentially withsystem size. This massive degeneracy is lifted at any non-zero $\lambda$ butsome special linear combinations that simultaneously diagonalize ${\cal O}_{\rmkin}$ and ${\cal O}_{\rm pot}$ survive as quantum many-body scars, suggestingan ``order-by-disorder'' mechanism in the Hilbert space. We give evidence forsuch scars and show their dynamical consequences on two-leg ladders with up to$56$ spins, which may be tested using available proposals of quantumsimulators. Results on wider ladders point towards their presence in twodimensions as well.

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