Universal witnesses of vanishing energy gap

This is the authors' abstract. We don't add key points for this paper.

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 an upper bound for the energy gap of a Hamiltonian H 0 based on properties of the set of expectation values of H 0 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.