Third-order strong-coupling impurity solver for real-frequency DMFT: Accurate spectral functions for antiferromagnetic and photo-doped states

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