Abstract
Energy gap, the difference between the energy of the ground state of a given Hamiltonian and the energy of its first excited state, is a parameter of a critical importance in analysis of phase transitions and adiabatic quantum computation. We present a concrete technique to determine the upper bound for the energy gap of a Hamiltonian H₀ based on properties of the set of expectation values of H₀ and an additional auxiliary Hamiltonian V. This formalism can be applied to obtain an effective criterion of gaplessness, which we illustrate with a concrete example of the XY model -- a physical system with vanishing energy gap.