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We solve the nonequilibrium dynamical mean-field theory (DMFT) using matrixproduct states (MPS). This allows us to treat much larger bath sizes and bythat reach substantially longer times (factor $\sim$ 2 -- 3) than with exactdiagonalization. We show that the star geometry of the underlying impurityproblem can have substantially better entanglement properties than thepreviously favoured chain geometry. This has immense consequences for theefficiency of an MPS-based description of general impurity problems: in thecase of equilibrium DMFT, it leads to an orders-of-magnitude speedup. Weintroduce an approximation for the two-time hybridization function that usestime-translational invariance, which can be observed after a certain relaxationtime after a quench to a time-independent Hamiltonian.

Solving nonequilibrium dynamical mean-field theory using matrix product states