  This paper demonstrates the application of semidefinite programming to
lattice field theories, showcasing spin chains and lattice scalar field theory.
Requiring expectation values of manifestly positive semi-definite operators to
be non-negative results in a lower bound on the ground-state energy of any
quantum mechanical system, which can be made arbitrarily tight for systems
described by finite-dimensional Hilbert spaces. Such bounds can be obtained
directly in the infinite-volume limit. The process of optimizing these lower
bounds also yields estimates for a chosen set of expectation values in the
ground state.
