  Symmetric mass generation (SMG) insulators are interaction-driven,
featureless Mott insulating states in quantum many-body fermionic systems.
Recent advancements suggest that zeros in the fermion Green's function could
lead to non-vanishing negative optical conductivity in SMG insulators, even
below the charge excitation gap. This study explores the origin of this unusual
behavior through the lens of pole-zero duality, highlighting a critical issue
where the current operator becomes unbounded, rendering the response function
unphysical. By employing a lattice model, we derive a well-behaved lattice
regularization of the current operator, enabling a detailed study of optical
conductivity in SMG insulators. Utilizing both analytical and numerical
methods, including strong-coupling expansions, we confirm that SMG insulators
exhibit no optical conductivity at low energies below the charge gap,
effectively resolving the paradox. This work not only deepens our understanding
of quantum many-body phenomena but also lays a robust theoretical groundwork
for future experimental explorations of SMG materials.
