  It has recently been established that quantum many-body scarring can prevent
the thermalisation of some isolated quantum systems, starting from certain
initial states. One of the first models to show this was the so-called PXP
Hamiltonian, which was used to theoretically model an experiment on a chain of
strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian
is a set of dynamical constraints that make certain states inaccessible to the
dynamics. In this paper we construct a class of spin chain models that are
parameterised by a discrete variable $\ell$ that controls the "strength" of a
dynamical constraint. We show that by increasing $\ell$ the constraint becomes
weaker, in the sense that fewer states are excluded from the dynamics. The PXP
Hamiltonian is special case for $\ell = 2$. By weakening the constraint to
$\ell \geq 4$, however, we find a more extreme version of quantum scarring than
in the PXP Hamiltonian, with the number of scar states growing exponentially in
the system size.
