  We construct a one-dimensional local spin Hamiltonian with an intrinsically
non-local, and therefore anomalous, global $\mathbb{Z}_2$ symmetry. The model
is closely related to the quantum Ising model in a transverse magnetic field,
and contains a parameter that can be tuned to spontaneously break the non-local
$\mathbb{Z}_2$ symmetry. The Hamiltonian is constructed to capture the
unconventional properties of the domain walls in the symmetry broken phase.
Using uniform matrix product states, we obtain the phase diagram that results
from condensing the domain walls. We find that the complete phase diagram
includes a gapless phase that is separated from the ordered ferromagnetic phase
by a Berezinskii-Kosterlitz-Thouless transition, and from the ordered
antiferromagnetic phase by a first order phase transition.
