Reply to “Comment on ‘${\mathbb{Z}}_2$-slave-spin theory for strongly correlated fermions’”

We show that the physical subspace in the ${\mathbb{Z}}_2$-slave-spin theory is conserved under the time evolution of the system. Thus, when restricted to the physical subspace, this representation gives a complete and consistent description of the original problem. In addition, we review two known examples from the existing literature in which the projection onto the physical subspace can be relaxed: (i) the noninteracting limit in any dimension at half-filling and (ii) the interacting model in the infinite-dimensional limit at half-filling. In both cases, physical observables are correctly obtained without explicit treatment of the constraints which define the physical subspace. In these examples, correct results are obtained, despite the fact that unphysical states enter the solution.