  The high level of control and precision achievable in current synthetic
quantum matter setups has enabled first attempts at quantum-simulating various
intriguing phenomena in condensed matter physics, including those probing
thermalization or its absence in closed quantum systems. In a recent work
[Desaules \textit{et al.} [arXiv:2203.08830], we have shown that quantum
many-body scars -- special low-entropy eigenstates that weakly break ergodicity
in nonintegrable systems -- arise in spin-$S$ quantum link models that converge
to $(1+1)-$D lattice quantum electrodynamics (Schwinger model) in the
Kogut--Susskind limit $S\to\infty$. In this work, we further demonstrate that
quantum many-body scars exist in a truncated version of the Schwinger model,
and are qualitatively more prominent than their counterparts in spin-$S$
quantum link models. We illustrate this by, among other things, performing a
finite-$S$ scaling analysis that strongly suggests that scarring persists in
the truncated Schwinger model in the limit $S\to\infty$. Although it does not
asymptotically converge to the Schwinger model, the truncated formulation is
relevant to synthetic quantum matter experiments, and also provides fundamental
insight into the nature of quantum many-body scars, their connection to lattice
gauge theories, and the thermalization dynamics of the latter. Our conclusions
can be readily tested in current cold-atom setups.
