Null bootstrap for non-Hermitian Hamiltonians

Abstract

A stable physical system has an energy spectrum that is bounded from below. For quantum systems, the dangerous states of unboundedly low energies should decouple and become null. We propose the principle of nullness and apply it to the bootstrap study of Hermitian and non-Hermitian anharmonic oscillators.

Comments: v4: 8 pages, 3 figures, title changed in accord to the published version (but also applies to Hermitian Hamiltonians!), Fig.3 added about the relation between the positive and the null bootstrap, footnote 19 added about the double well potential, discussion improved; v3: a new section added about ladder operators and matrix elements, minor improvements, typos corrected, references added