Nonlinear Drude weight of the one-dimensional Hubbard model
Abstract
We investigate nonlinear Drude weights (NLDWs) in the one-dimensional repulsive Hubbard model at zero temperature by combining exact Bethe-ansatz calculations with low-energy effective field theory. At quarter filling, we first derive the strong-coupling expansion of the NLDWs and confirm it numerically over a wide range of interaction strength. We then compare the numerical results with the prediction of the Tomonaga-Luttinger liquid (TLL) description including irrelevant perturbations. While band-curvature corrections yield finite contributions to higher-order NLDWs, the Umklapp interaction predicts divergent NLDWs when the order n of the Drude weight exceeds a threshold determined by the TLL parameter. In contrast, finite-size scaling of the exact Bethe-ansatz results indicates that all calculated NLDWs remain finite in the thermodynamic limit, revealing a discrepancy between the exact results and the predictions of the low-energy effective field theory. At half filling, we analyze the finite-size scaling of the NLDWs across the Mott metal-insulator transition. We derive their asymptotic behavior in the insulating phase and propose a hyperscaling ansatz for NLDWs near the critical point, which is verified numerically. Our results clarify the interaction dependence and critical scaling of nonlinear transport coefficients in the one-dimensional Hubbard model and highlight limitations of the conventional low-energy effective description for higher-order transport.
Related
- Local wave-packet spectroscopy of the Drude weight in Tomonaga-Luttinger liquids
- Universal Drude Weights in One-dimensional Repulsive Fermi Gas
- Weyl superconductivity from Feshbach resonance in the three-dimensional repulsive Hubbard model
- Pairing order and condensate fraction across the BCS-BEC crossover in the two-dimensional attractive Hubbard model
- Fermion bag study of the two-dimensional Majorana-Hubbard model at finite hopping
BibTeX
@misc{iwasaki2026nonlinear,
title = {{Nonlinear Drude weight of the one-dimensional Hubbard model}},
author = {Tetsuya Iwasaki and Hosho Katsura},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.20269},
eprint = {2608.20269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.20269},
}
RIS
TY - UNPB
TI - Nonlinear Drude weight of the one-dimensional Hubbard model
AU - Tetsuya Iwasaki
AU - Hosho Katsura
PY - 2026
DA - 2026/09/04
PB - arXiv
DO - 10.48550/arxiv.2608.20269
UR - https://arxiv.org/abs/2608.20269
AB - We investigate nonlinear Drude weights (NLDWs) in the one-dimensional repulsive Hubbard model at zero temperature by combining exact Bethe-ansatz calculations with low-energy effective field theory. At quarter filling, we first derive the strong-coupling expansion of the NLDWs and confirm it numerically over a wide range of interaction strength. We then compare the numerical results with the prediction of the Tomonaga-Luttinger liquid (TLL) description including irrelevant perturbations. While band-curvature corrections yield finite contributions to higher-order NLDWs, the Umklapp interaction predicts divergent NLDWs when the order n of the Drude weight exceeds a threshold determined by the TLL parameter. In contrast, finite-size scaling of the exact Bethe-ansatz results indicates that all calculated NLDWs remain finite in the thermodynamic limit, revealing a discrepancy between the exact results and the predictions of the low-energy effective field theory. At half filling, we analyze the finite-size scaling of the NLDWs across the Mott metal-insulator transition. We derive their asymptotic behavior in the insulating phase and propose a hyperscaling ansatz for NLDWs near the critical point, which is verified numerically. Our results clarify the interaction dependence and critical scaling of nonlinear transport coefficients in the one-dimensional Hubbard model and highlight limitations of the conventional low-energy effective description for higher-order transport.
ER -