Semidefinite programs for few-nucleon systems

In a quantum mechanical system, the norm of any state must be non-negative; equivalently, for any observable O, the expectation value 〈O^†O〉must be non-negative. It was recently proposed (by Han, Hartnoll, and Kruthoff; later explored by Berenstein and Hulsey among many others) to turn this observation into a computational method---sometimes terms the quantum-mechanical bootstrap---for probing the ground state of an arbitrary Hamiltonian. The result is a semidefinite program (a particular convex optimization task) which, when solved, yields a lower bound on the ground-state energy, along with estimates of other expectation values in the ground state. The same approach has been applied to lattice field theories, including at finite fermion density. In this talk we show how the method may be applied to few-nucleon systems using a Hamiltonian from pionless EFT.