Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory

TL;DR

This paper introduces configuration interaction (CI) approximations as polynomial-cost solvers for quantum impurity models in dynamical mean-field theory, offering controllable errors and near-exact results with significantly reduced computational effort.

Contribution

It demonstrates how CI approximations can serve as efficient, controllable, and accurate solvers for DMFT, extending the applicability to larger and more complex impurity models.

Findings

CI approximations achieve near-exact ED results at a fraction of the cost.

CI methods effectively handle large orbital numbers and complex interactions.

Convergence of bath representation in cluster DMFT is demonstrated with 24 bath orbitals.

Abstract

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$ cluster DMFT of the 2D Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including "difficult" regimes, such as in the pseudogap phase of the 2D Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24 bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.