Interaction expansion inchworm Monte Carlo solver for lattice and impurity models

TL;DR

This paper introduces a generalized interaction expansion inchworm Monte Carlo method capable of handling complex multi-orbital impurity models, improving over some existing algorithms in certain scenarios.

Contribution

The paper extends the inchworm quantum Monte Carlo method to the interaction expansion, broadening its applicability to complex impurity and lattice models.

Findings

Outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion.

Remains inferior to hybridization expansion and auxiliary field algorithms for studied systems.

Does not encounter convergence issues to unphysical fixed points like some other methods.

Abstract

Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion and explore its application to typical single- and multi-orbital problems encountered in investigations of impurity and lattice models. Our implementation generically outperforms bare and bold-line quantum Monte Carlo algorithms in the interaction expansion. So far, for the systems studied here, it remains inferior to the more specialized hybridization expansion and auxiliary field algorithms. The problem of convergence to unphysical fixed points, which hampers so-called bold-line methods, is not encountered in inchworm Monte Carlo.