  We study numerically the evolution of energy-level statistics as an
integrability-breaking term is added to the XXZ Hamiltonian. For finite-length
chains, physical properties exhibit a cross-over from behavior resulting from
the Poisson level statistics characteristic of integrable models to behavior
corresponding to the Wigner-Dyson statistics characteristic of the
random-matrix theory used to describe chaotic systems. Different measures of
the level statistics are observed to follow different crossover patterns. The
range of numerically accessible system sizes is too small to establish with
certainty the scaling with system size, but the evidence suggests that in a
thermodynamically large system an infinitesimal integrability breaking would
lead to Wigner-Dyson behavior.
