The spectral gap problem—whether the Hamiltonian of a quantum many-body problem is gapped or gapless—is rigorously proved to be undecidable; there exists no algorithm to determine whether an arbitrary quantum many-body model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.
- Toby S. Cubitt
- David Perez-Garcia
- Michael M. Wolf
