Hybrid Monte Carlo for the extended Kane-Mele-Hubbard model
Abstract
The Hubbard model offers a powerful minimal description of strongly correlated electrons in molecules and materials, yet it neglects effects observed in nature that give rise to a much richer variety of physics. For instance, including nonlocal interactions introduces a competition between strongly correlated phases, while incorporating spin-orbit coupling (SOC) can lead to the emergence of exotic topological phases. Seeking a more realistic platform for simulating graphene and, potentially, related materials such as transition metal dichalcogenides (TMDs), we therefore consider the extended Kane-Mele-Hubbard model, which features a Kane-Mele SOC term and nearest-neighbor interactions. Simulating this model is particularly challenging once the nonlocal interactions become dominant over the on-site Hubbard interaction, as a severe sign problem arises already at half filling, leaving this regime largely unexplored. In this work, we develop continuous auxiliary field formulations of the model, suitable for treatment with the Hybrid Monte Carlo (HMC) algorithm. Using these formulations, we characterize the sign problem across the model's parameter space and establish where simulations are feasible, as a first step toward the full phase diagram.
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BibTeX
@misc{temmen2026hybrid,
title = {{Hybrid Monte Carlo for the extended Kane-Mele-Hubbard model}},
author = {Finn L. Temmen and Thomas Luu and Johann Ostmeyer and Lin Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32458},
eprint = {2610.32458},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32458},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Hybrid Monte Carlo for the extended Kane-Mele-Hubbard model
AU - Finn L. Temmen
AU - Thomas Luu
AU - Johann Ostmeyer
AU - Lin Wang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32458
UR - https://arxiv.org/abs/2610.32458
AB - The Hubbard model offers a powerful minimal description of strongly correlated electrons in molecules and materials, yet it neglects effects observed in nature that give rise to a much richer variety of physics. For instance, including nonlocal interactions introduces a competition between strongly correlated phases, while incorporating spin-orbit coupling (SOC) can lead to the emergence of exotic topological phases. Seeking a more realistic platform for simulating graphene and, potentially, related materials such as transition metal dichalcogenides (TMDs), we therefore consider the extended Kane-Mele-Hubbard model, which features a Kane-Mele SOC term and nearest-neighbor interactions. Simulating this model is particularly challenging once the nonlocal interactions become dominant over the on-site Hubbard interaction, as a severe sign problem arises already at half filling, leaving this regime largely unexplored. In this work, we develop continuous auxiliary field formulations of the model, suitable for treatment with the Hybrid Monte Carlo (HMC) algorithm. Using these formulations, we characterize the sign problem across the model's parameter space and establish where simulations are feasible, as a first step toward the full phase diagram.
ER -