Reply to "Comment on 'Z2-slave-spin theory for strongly correlated fermions' "

TL;DR

This paper clarifies the validity of the Z2-slave-spin theory by demonstrating the conservation of the physical subspace during evolution and reviewing cases where constraints can be relaxed without affecting observable results.

Contribution

It proves the physical subspace is conserved in Z2-slave-spin theory and reviews instances where constraints can be relaxed, simplifying calculations.

Findings

Physical subspace is conserved under time evolution.

Correct physical observables are obtained even when constraints are relaxed.

Relaxation of constraints is valid in specific limits like non-interacting and infinite dimensions.

Abstract

We show that the physical subspace in the Z2-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 non-interacting 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.