Universal witnesses of vanishing energy gap

Energy gap, the difference between energy of ground state a given Hamiltonian and its first excited state, is parameter critical importance in analysis phase transitions adiabatic quantum computation. We present concrete technique to determine upper bound for gap $H_0$ based on properties set expectation values an additional auxiliary $V$. This formalism can be applied obtain effective criterion gaplessness, which we illustrate with example XY model -- physical system vanishing gap.