Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations

TL;DR

This paper introduces a numerically exact Inchworm Monte Carlo method capable of solving multiorbital quantum impurity problems with general interactions and hybridizations, overcoming the sign problem in equilibrium simulations.

Contribution

The authors develop and demonstrate a new Monte Carlo approach that overcomes the sign problem for equilibrium multiorbital impurity models, enabling more accurate simulations.

Findings

Method overcomes the sign problem at various temperatures.

Enables simulations without hybridization or interaction truncation.

Eliminates a key bottleneck in ab initio embedding calculations.

Abstract

We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of ab initio embedding problems.