一维哈伯德模型的非线性德鲁德权重
Nonlinear Drude weight of the one-dimensional Hubbard model
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中文总结 AI 辅助
本研究结合贝特-ansatz计算与低能有效场论，探究一维哈伯德模型的非线性德鲁德权重，发现低能理论对高阶输运的预测存在偏差，明确了非线性输运系数的标度规律。
中文摘要 AI 辅助
我们结合精确的贝特- ansatz（Bethe-ansatz）计算与低能有效场论，研究一维排斥哈伯德模型中的非线性德鲁德权重（NLDWs）。在四分之一填充时，我们首先推导NLDWs的强耦合展开式，并在宽相互作用强度范围内通过数值计算予以验证。随后，我们将数值结果与包含无关微扰的托莫纳加-卢廷格液体（TLL）描述的预测进行比较：尽管带曲率修正对高阶NLDWs产生有限贡献，但当德鲁德权重的阶数n超过TLL参数确定的阈值时，Umklapp相互作用会预测NLDWs发散；相比之下，精确贝特- ansatz结果的有限尺寸标度表明，所有计算得到的NLDWs在热力学极限下均保持有限，这揭示了精确结果与低能有效场论预测之间的不一致。在半填充时，我们分析NLDWs在莫特金属-绝缘体相变处的有限尺寸标度，推导其绝缘相中的渐近行为，并提出临界点附近NLDWs的超标度假设，该假设通过数值计算得到验证。我们的结果阐明了一维哈伯德模型中非线输运系数的相互作用依赖性和临界标度，并凸显了传统低能有效描述对高阶输运的局限性。
英文摘要
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.
发表机构
- The University of Tokyo（东京大学）
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