We present a real-frequency third-order strong-coupling impurity solver which employs quantics tensor cross interpolation (QTCI) for an efficient evaluation of the diagram weights. Applying the method to dynamical mean-field theory (DMFT) calculations of the single-band Hubbard model on the Bethe lattice, we clarify the interaction and temperature range in which the third-order approach yields accurate results. Since the calculations are implemented on the real-time/frequency axis, the detailed structure of spectral functions can be obtained without analytical continuation, as we demonstrate with examples for paramagnetic, antiferromagnetic, and photodoped states. Our work establishes a viable path toward high-order, real-frequency impurity solvers for both equilibrium and nonequilibrium DMFT studies.

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• Antiferromagnetism
• Density of states
• Paramagnetism
• Approximation methods for many-body systems
• Diagrammatic methods
• Dynamical mean field theory
• Green's function methods
• Hubbard model
• Single impurity model