Benchmarking Non-perturbative Many-Body Approaches in the Exactly Solvable Hatsugai-Kohmoto Model

TL;DR

This paper uses the exactly solvable Hatsugai-Kohmoto model to benchmark and evaluate the accuracy of non-perturbative many-body approaches like GW, HGW, and SGW in describing strongly correlated electron systems.

Contribution

It introduces the HK model as a new benchmark platform for many-body methods and reveals the accurate Mott physics solution branch within the GW approximation.

Findings

GW exhibits a new solution branch capturing Mott physics

HGW accurately describes charge response functions

SGW performs well for spin correlations

Abstract

The accurate simulation of strongly correlated electron systems remains a central challenge in condensed matter physics, motivating the development of various non-perturbative many-body methods. Such methods are typically benchmarked against the numerical exact determinant quantum Monte Carlo (DQMC) in the Hubbard model; however, DQMC is limited by the fermionic sign problem and the uncertainties of numerical analytic continuation. To address these issues, we use the exactly solvable Hatsugai-Kohmoto (HK) model as a benchmarking platform to evaluate three many-body approximations: $GW$, $HGW$, and $SGW$. We compare the Green's functions, spectral functions, and response functions obtained from these approximations with the exact solutions. Our analysis shows that the $GW$ approximation, often considered insufficient for describing strong correlation, exhibits a previously unreported solution branch that accurately reproduces Mott physics in the HK model. In addition, using a covariant formalism, we find that $HGW$ provides an accurate description of charge response, while $SGW$ performs well for spin correlations. Overall, our work demonstrates that the HK model can effectively benchmark many-body approximations and helps refine the understanding of $GW$ methods in strongly correlated regimes.