  As a consequence of Bloch's theorem, the numerical computation of the
fermionic ground state density matrices and energies of periodic Schrodinger
operators involves integrals over the Brillouin zone. These integrals are
difficult to compute numerically in metals due to discontinuities in the
integrand. We perform an error analysis of several widely-used quadrature rules
and smearing methods for Brillouin zone integration. We precisely identify the
assumptions implicit in these methods and rigorously prove error bounds.
Numerical results for two-dimensional periodic systems are also provided. Our
results shed light on the properties of these numerical schemes, and provide
guidance as to the appropriate choice of numerical parameters.
