State- and superstate-sampling in hybridization-expansion continuous-time quantum Monte Carlo

TL;DR

This paper introduces a fragment-based superstate sampling method for hybridization-expansion continuous-time quantum Monte Carlo, significantly improving efficiency and sign preservation in complex multi-orbital impurity models.

Contribution

The authors develop a novel superstate sampling technique that enhances efficiency and sign stability in quantum Monte Carlo simulations with many orbitals and complex interactions.

Findings

Improved sampling efficiency in multi-orbital models.

Preservation of fermionic sign during sampling.

Quantitative analysis of spin-freezing crossover near Mott transition.

Abstract

Due to the intrinsic complexity of the quantum many-body problem, quantum Monte Carlo algorithms and their corresponding Monte Carlo configurations can be defined in various ways. Configurations corresponding to few Feynman diagrams often lead to severe sign problems. On the other hand, computing the configuration weight becomes numerically expensive in the opposite limit in which many diagrams are grouped together. Here we show that for continuous-time quantum Monte Carlo in the hybridization expansion the efficiency can be substantially improved by dividing the local impurity trace into fragments, which are then sampled individually. For this technique, which also turns out to preserve the fermionic sign, a modified update strategy is introduced in order to ensure ergodicity. Our (super)state sampling is particularly beneficial to calculations with many $d$-orbitals and general local interactions, such as full Coulomb interaction. For illustration, we reconsider the simple albeit well-known case of a degenerate three-orbital model at low temperatures. This allows us to quantify the coherence properties of the "spin-freezing" crossover, even close to the Mott transition.