Imaginary-time matrix product state impurity solver in a real material calculation: Spin-orbit coupling in Sr$_2$RuO$_4$

TL;DR

This paper introduces a zero-temperature imaginary-time matrix product state impurity solver for DMFT calculations that accurately incorporates spin-orbit coupling in Sr$_2$RuO$_4$, overcoming limitations of traditional methods.

Contribution

It presents a novel MPS-based impurity solver capable of handling SOC at zero temperature, enabling more realistic DMFT calculations for complex materials.

Findings

SOC effects are consistent with high-temperature results at low temperature.

Interactions enhance the effective SOC in Sr$_2$RuO$_4$.

The MPS solver requires algorithmic improvements for realistic material calculations.

Abstract

Using an imaginary-time matrix-product state (MPS) based quantum impurity solver we perform a realistic dynamical mean-field theory (DMFT) calculation combined with density functional theory (DFT) for Sr$_2$RuO$_4$. We take the full Hubbard-Kanamori interactions and spin-orbit coupling (SOC) into account. The MPS impurity solver works at essentially zero temperature in the presence of SOC, a regime of parameters currently inaccessible to continuous-time quantum Monte Carlo (CTQMC) methods, due to a severe sign problem. We show that earlier results obtained at high temperature, namely that the diagonal self-energies are nearly unaffected by SOC and that interactions lead to an effective enhancement of the SOC, hold even at low temperature. We observe that realism makes the numerical solution of the impurity model with MPS much more demanding in comparison to earlier works on Bethe lattice models, requiring several algorithmic improvements.