Twisting the Hubbard model into the Momentum-Mixing Hatsugai-Kohmoto Model

TL;DR

This paper introduces the momentum-mixing Hatsugai-Kohmoto (MMHK) model, a new approach that deforms into the Hubbard model, accurately capturing Mott physics with fewer momenta and offering an efficient tool for studying strongly correlated materials.

Contribution

The authors develop the MMHK model by systematically reintroducing momentum mixing, enabling accurate approximation of the Hubbard model's ground state with minimal momenta.

Findings

MMHK reproduces the Hubbard model's ground state energy within 1% using only ten mixed momenta.

Convergence of the MMHK model scales as 1/n^2, outperforming standard finite-cluster methods.

Results on a square lattice match state-of-the-art simulations with few momenta.

Abstract

The Hubbard model is a standard theoretical tool for studying materials with strong electron-electron interactions, such as the cuprate superconductors. Unfortunately, interaction-driven phenomena such as the transition into the strongly correlated Mott insulator phase are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai-Kohmoto model displays similar Mott physics. Here we show how the Hatsugai-Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically re-introduce all the momentum mixing the original Hatsugai-Kohmoto model omits. This can be accomplished by grouping $n$-momenta into a cell and hybridizing them resulting in the momentum-mixing Hatsugai-Kohmoto (MMHK) model. We recover the Bethe ansatz ground state energy of the one-dimensional Hubbard model to within 1$\%$ from only ten mixed momenta. Overall the convergence scales as $1/n^2$ as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe the MMHK model offers an alternative tool for strongly correlated quantum matter.