Volume 136, Number 3, November 2021
|Number of page(s)||7|
|Published online||25 February 2022|
Universal witnesses of vanishing energy gap
1 Institute of Theoretical Physics, Uniwersytet Jagielloński - 30-348 Kraków, Poland
2 Centrum Fizyki Teoretycznej PAN - 02-668 Warszawa, Poland
Received: 21 May 2021
Accepted: 3 November 2021
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 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.
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