# Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models

## TL;DR

This paper introduces a basis optimization method to reduce the sign problem in quantum Monte Carlo simulations of spin-orbit-coupled multi-orbital Hubbard models, enabling more efficient material simulations.

## Contribution

The authors propose a stochastic basis optimization approach that significantly improves the average sign in CTQMC simulations for spin-orbit-coupled systems, enhancing computational efficiency.

## Key findings

- Bonding-antibonding basis improves average sign
- Stochastic optimization finds near-optimal basis
- Enables more efficient DMFT simulations

## Abstract

We present a strategy to alleviate the sign problem in continuous-time quantum Monte Carlo (CTQMC) simulations of the dynamical-mean-field-theory (DMFT) equations for the spin-orbit-coupled multiorbital Hubbard model. We first identify the combinations of rotationally invariant Hund coupling terms present in the relativistic basis which lead to a severe sign problem. Exploiting the fact that the average sign in CTQMC depends on the choice of single-particle basis, we propose a bonding-antibonding basis $V_{j3/2\mathrm{BA}}$ which shows an improved average sign compared to the widely used relativistic basis for most parameter sets investigated. We then generalize this procedure by introducing a stochastic optimization algorithm that exploits the space of single-particle bases and show that $V_{j3/2\mathrm{BA}}$ is very close to optimal within the parameter space investigated. Our findings enable more efficient DMFT simulations of materials with strong spin-orbit coupling.