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Energy gap, the difference between the energy of the ground state of a givenHamiltonian and the energy of its first excited state, is a parameter of acritical importance in analysis of phase transitions and adiabatic quantumcomputation. We present a concrete technique to determine the upper bound forthe energy gap of a Hamiltonian $H_0$ based on properties of the set ofexpectation values of $H_0$ and an additional auxiliary Hamiltonian $V$. Thisformalism can be applied to obtain an effective criterion of gaplessness, whichwe illustrate with a concrete example of the XY model -- a physical system withvanishing energy gap.

Universal witnesses of vanishing energy gap