  We present a sign-problem free quantum Monte Carlo study of a model that
exhibits quantum phase transitions without symmetry breaking and associated
changes in the size of the Fermi surface. The model is an Ising gauge theory on
the square lattice coupled to an Ising matter field and spinful `orthogonal'
fermions at half-filling, both carrying Ising gauge charges. In contrast to
previous studies, our model hosts an electron-like, gauge-neutral fermion
excitation providing access to Fermi liquid phases. One of the phases of the
model is a previously studied orthogonal semi-metal, which has $\mathbb{Z}_2$
topological order, and Luttinger-volume violating Fermi points with gapless
orthogonal fermion excitations. We elucidate the global phase diagram of the
model: along with a conventional Fermi liquid phase with a large
Luttinger-volume Fermi surface, we also find a `deconfined' Fermi liquid in
which the large Fermi surface co-exists with fractionalized excitations. We
present results for the electron spectral function, showing its evolution from
the orthogonal semi-metal with a spectral weight near momenta $\{\pm \pi/2, \pm
\pi/2\}$, to a large Fermi surface.
