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arXiv · 2104.13884

Universal witnesses of vanishing energy gap

Konrad Szymański·Karol Życzkowski
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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 $H_0$ 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.

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Konrad Szymański, Karol Życzkowski. 2021-04-28. Universal witnesses of vanishing energy gap. https://doi.org/10.1209/0295-5075%2Fac35f4

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