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

TL;DR

This paper introduces a tree tensor-network impurity solver for multiorbital systems, capable of accurately computing spectral functions and correlation functions directly on the real-time axis, with applications to Sr$_2$RuO$_4$.

Contribution

The authors develop a novel tensor-network impurity solver that efficiently captures entanglement and symmetry, enabling detailed real-time spectral and correlation function calculations for complex multiorbital materials.

Findings

Successfully resolves low-energy quasiparticle spectra and high-energy multiplet excitations in Sr$_2$RuO$_4$.

Shows spin-orbit coupling has minor effects on orbital-diagonal spectral functions.

Demonstrates the solver's ability to handle off-diagonal Green's functions and compute dynamical correlations.

Abstract

We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diagonal Green's functions. For the archetypal correlated Hund's metal Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related to the van Hove singularity and the high-energy atomic multiplet excitations can be faithfully resolved. In particular, we show that while the spin-orbit coupling has only minor effects on the orbital-diagonal one-particle spectral functions, it has a more profound impact on the low-energy spin and orbital response functions.