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

TL;DR

This paper uncovers a new mechanism for quantum many-body scars in a $U(1)$ lattice gauge theory, demonstrating their existence in ladder systems and potential relevance in higher dimensions, with implications for quantum simulation.

Contribution

It introduces a novel 'order-by-disorder' mechanism for quantum scars in a constrained gauge theory, supported by numerical evidence in ladder systems.

Findings

Existence of exact mid-spectrum zero modes at zero coupling

Special linear combinations form quantum many-body scars

Dynamical effects observed in two-leg ladder systems

Abstract

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. This massive degeneracy is lifted at any non-zero $\lambda$ 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.