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

Understand

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 $H={\cal O}_{\rm kin}+\lambda {\cal O}_{\rm pot}$, 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 $\lambda=0$ whose number grows exponentially with system size.