  We develop a Markovian master equation in the Lindblad form that enables the
efficient study of a wide range of open quantum many-body systems that would be
inaccessible with existing methods. The validity of the master equation is
based entirely on properties of the bath and the system-bath coupling, without
any requirements on the level structure within the system itself. The master
equation is derived using a Markov approximation that is distinct from that
used in earlier approaches. We provide a rigorous bound for the error induced
by this Markov approximation; the error is controlled by a dimensionless
combination of intrinsic correlation and relaxation timescales of the bath. Our
master equation is accurate on the same level of approximation as the
Bloch-Redfield equation. In contrast to the Bloch-Redfield approach, our
approach ensures preservation of the positivity of the density matrix. As a
result, our method is robust, and can be solved efficiently using stochastic
evolution of pure states (rather than density matrices). We discuss how our
method can be applied to static or driven quantum many-body systems, and
illustrate its power through numerical simulation of a spin chain that would be
challenging to treat by existing methods.
