Universal witnesses of vanishing energy gap

• URL: http://arxiv.org/abs/2104.13884v1
• Date: Wed, 28 Apr 2021 17:06:05 GMT
• Title: Universal witnesses of vanishing energy gap
• Authors: Konrad Szyma\'nski, Karol \.Zyczkowski
• Abstract summary: Energy gap is the difference between the energy of the ground state of a given Hamiltonian and the energy of its first excited state. We present a technique to determine the upper bound for the energy gap of a Hamiltonian. We illustrate with a concrete example of the XY model -- a physical system with vanishing energy gap.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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