Universal witnesses of vanishing energy gap

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.

7 pages, 4 figures

References in corpus (8)

• Variational quantum algorithms for discovering Hamiltonian spectra
• Topological theory of Lieb-Schultz-Mattis theorems in quantum spin systems
• State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems
• Spectral gaps of frustration-free spin systems with boundary
• Numerical shadow and geometry of quantum states
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Observing geometry of quantum states in a three-level system
• Separability gap and large deviation entanglement criterion