  We present an expression for the spectral gap, opening up new possibilities
for performing and accelerating spectral calculations of quantum many-body
systems. We develop and demonstrate one such possibility in the context of
tensor network simulations. Our approach requires only minor modifications of
the widely used simple update method and is computationally lightweight
relative to other approaches. We validate it by computing spectral gaps of the
2D and 3D transverse-field Ising models and find strong agreement with
previously reported perturbation theory results.
