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We present a tree tensor-network impurity solver suited for generalmultiorbital systems. The network is constructed to efficiently capture theentanglement structure and symmetry of an impurity problem. The solver worksdirectly on the real-time/frequency axis and generates spectral functions withenergy-independent resolution of the order of one percent of the correlatedbandwidth. Combined with an optimized representation of the impurity bath, itefficiently solves self-consistent dynamical mean-field equations andcalculates various dynamical correlation functions for systems withoff-diagonal Green's functions. For the archetypal correlated Hund's metalSr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra relatedto the van Hove singularity and the high-energy atomic multiplet excitationscan be faithfully resolved. In particular, we show that while the spin-orbitcoupling has only minor effects on the orbital-diagonal one-particle spectralfunctions, it has a more profound impact on the low-energy spin and orbitalresponse functions.

Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr$_2$RuO$_4$