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In this work, we present a nonlocal expansion scheme to study correlatedelectron systems aiming at a better description of its spatial fluctuations atall length scales. Taking the nonlocal coupling as a perturbation to the localdegrees of freedom, we show that the nonlocality in the self-energy functioncan be efficiently constructed from the coupling between local fluctuations. Itcan provide one unified framework to incorporate nonlocality to both orderedand disordered correlated many-body fermion systems. In this application, weprove that the dual-fermion approach can be understood as a special case ofthis nonlocal expansion scheme. The scheme presented in this work isconstructed without introducing any dual variable, in which the interactingnature and the correlated behaviors of the lattice fermions have a clearphysics correspondence. Thus, in this special case, the equivalence of thedual-fermion approach to the nonlocal expansion scheme beautifully reveals thephysics origin of the dual variables. We show that the noninteractingdual-fermion Green's function corresponds exactly to a nonlocal coupling of thelattice fermion renormalized by the local single-particle charge fluctuations,and the dual-fermion self-energy behaves as the one-particle fully irreduciblecomponents of the lattice Green's function. Not only limited to this specificexample, the nonlocal expansion scheme presented in this work can also beapplied to other problems depending on the choice of the local degrees offreedom.

Hidden physics in the dual-fermion approach - a special case of a non-local expansion scheme