Bootstrapping Bloch bands

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of mechanical problems, such as single particle Schrödinger equation with an anharmonic potential. The core bootstrap methods builds on exact recursion relations arbitrary moments some operator use adequate set positivity criteria. We extend this methodology models continuous Bloch band spectra, by considering a in periodic cosine find that structure can be obtained accurately provided uses involving both position momentum variables. also introduce several new techniques apply generally other studies. First, we devise trick reduce one unit dimensionality search space variables parametrizing bootstrap. Second, employ reconstruct distribution probability allowing compute observables are analytic functions canonical This method is used extract momentum, quantity not readily available from itself.