Fermi-surface reconstruction without symmetry breaking

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.