  Quantum many-body systems are typically endowed with a tensor product
structure. This structure is inherited from probability theory, where the
probability of two independent events is the product of the probabilities. The
tensor product structure of a Hamiltonian thus gives a natural decomposition of
the system into independent smaller subsystems. Considering a particular
Hamiltonian and a particular tensor product structure, one can ask: is there a
basis in which this Hamiltonian has this desired tensor product structure? In
particular, we ask: is there a basis in which an arbitrary Hamiltonian has a
2-local form, i.e. it contains only pairwise interactions? Here we show, using
numerical and analytical arguments, that generic Hamiltonian (e.g. a large
random matrix) can approximately be written as a linear combination of two-body
interactions terms with high precision; that is the Hamiltonian is 2-local in a
carefully chosen basis. We show that these Hamiltonians are robust to
perturbations. Taken together, our results suggest a possible mechanism for the
emergence of locality from chaos.
