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We present an expression for the spectral gap, opening up new possibilitiesfor performing and accelerating spectral calculations of quantum many-bodysystems. We develop and demonstrate one such possibility in the context oftensor network simulations. Our approach requires only minor modifications ofthe widely used Simple Update method and is computationally lightweightrelative to other approaches. We validate it by computing spectral gaps of the2D and 3D transverse-field Ising models and find strong agreement withpreviously reported perturbation theory results.

Spectral Gaps of 2D and 3D Many-body Quantum Systems in the Thermodynamic Limit