  Many-body quantum systems present a rich phenomenology which can be
significantly altered when they are in contact with an environment. In order to
study such setups, a number of approximations are usually performed, either
concerning the system, the environment, or both. A typical approach for large
quantum interacting systems is to use master equations which are local,
Markovian, and in Lindblad form. Here, we present an implementation of the
Redfield master equation using matrix product states and operators. We show
that this allows us to explore parameter regimes of the many-body quantum
system and the environment which could not be probed with previous approaches
based on local Lindblad master equations. We also show the validity of our
results by comparing with the numerical exact thermofield-based chain-mapping
approach.
