Global becomes local: efficient many-body dynamics for global master equations

This Letter makes progress on the issue of global vs local master equations. Global master equations like the Redfield master equation (following from standard Born and Markov approximation) require a full diagonalization of the system Hamiltonian. This is especially challenging for interacting quantum many-body systems. We discuss a short-bath-correlation-time expansion in reciprocal (energy) space, leading to a series expansion of the jump operator, which avoids a diagonalization of the Hamiltonian. For a bath that is coupled locally to one site, this typically leads to an expansion of the global Redfield jump operator in terms of local operators. We additionally map the local Redfield master equation to a novel local Lindblad form, giving an equation which has the same conceptual advantages of traditional local Lindblad approaches while being applicable in a much broader class of systems. Our ideas give rise to a nonheuristic foundation of local master equations, which can be combined with established many-body methods.