Spectral gap (physics)
In quantum mechanics, the spectral gap of a system is the energy difference between its ground state and its first excited state. The mass gap is the spectral gap between the vacuum and the lightest particle. A Hamiltonian with a spectral gap is called a gapped Hamiltonian, and those that do not are called gapless.
In solid-state physics, the most important spectral gap is for the many-body system of electrons in a solid material, in which case it is often known as an energy gap.
In quantum many-body systems, ground states of gapped Hamiltonians have exponential decay of correlations.
In 2015 it was shown that the problem of determining the existence of a spectral gap is undecidable. The authors used an aperiodic tiling of quantum Turing machines and showed that this hypothetical material becomes gapped if and only if it halts.
