A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
This work develops a sequence of semidefinite programming (SDP) certificates to rigorously find lower bounds for the spectral gap of local qubit Hamiltonians. It uses a noncommutative polynomial optimization problem based on Lie algebra constraints to certify that the difference between the two smallest eigenvalues is bounded from below, providing a method to prove positive gaps in quantum systems.