[论文解读] Data for: "Waterfalls: umbilical cords at the birth of Hubbard bands"

Juraj Krsnik|arXiv (Cornell University)|Aug 23, 2024

Cuban History and Society被引用 1

一句话总结

该论文表明，水瀑布结构——角分辨光电子能谱中垂直且展宽的特征——在 Hubbard 模型中自然地由局域电子关联导致 Hubbard 带从准粒子带分离而产生。通过使用从第一性原理获得参数的动态平均场理论（DMFT），作者证明这些异常并非源于自旋涨落或声子，而是局域关联的直接结果，且在铜氧化物和镍氧化物中与实验数据高度吻合。

ABSTRACT

Context and methodology This repository contains raw data from the associated research work. It serves the purpose of aiding interested readers to reproduce the results of the related work and verify their validity. The research area in which this dataset is created is that of condensed matter, strongly correlated electron systems, ARPES, cuprates, and nickelates. This dataset was created using the w2dynamics code for DMFT calculations, the ana_cont package for analytic continuation, and the DGApy code for DGA calculations. Technical details For each figure there is a corresponding folder in data folder containing the data shown in the figure. Data files are of type hk, hdf5, npz, and txt and named logically after data they contain. Reading the data requires python (version 3.10.13, numpy version 1.26.0) with h5py (version 3.10.0). The detailed content of the data files can found in a README file. w2dynamics calculations DMFT calculations are done in three iterations, each involving different numbers of DMFT steps and statistics. Corresponding input files _Parameters_dmft_iter.in, _Parameters_dmft_iter_2.in, and _Parameters_dmft_stat.in can be found in the folder input_files/w2dynamics/, and are executed in that order. The output of the last iteration is contained in 1p-data.hdf5, including the self-energy on the Matsubara axis. DGApy calculations In addition to the single-particle data in 1p-data.hdf5, DGApy requires the two-particle DMFT data contained in g4iw_sym.hdf5. The corresponding input file _Parameters_vertex.in for w2dynamics can be found in input_files/w2dynamics/. Note that the DMFT output will contain the full Vertex.hdf5. To get g4iw_sym.hdf5 one needs to execute sym1b (part of DGApy) in the same folder where Vertex.hdf5 is located. The resulting self-energy on the Matsubara axis is contained in siwk_dga.npy files. ana_cont Analytical continuation of the self-energy to the real-frequency axis was performed using MaxEnt as implemented in the ana_cont python package; model for fitting was flat and chi2kink method was used to determine the hyperparameter alpha. For temperatures T = 100/t and T = 15/t, number of fermionic Matsubara frequencies taken was 800 and 200, while the real-frequency grid was taken to be linear with 1001 points in the range [-50,50]. Errors for DMFT self-energies can be found in 1p-data.hdf5, while for DGA results it is taken to be 1e-3; preblur was set to 1e-3 in all calculations. Analyically continued DMFT self-energy is located in self_energy.npz files, while analytically continued DGA self-energy in self_energy_nw1001_nk400_delta0.04.npy. Note that the interpolation in both momentum and frequency space may be employed to get better resolution. In addition, a constant imaginary part of 0.04 was added to the DGA self-energy to improve stability of results.

研究动机与目标

• 解决长期以来关于关联氧化物 ARPES 谱中高能水瀑布异常物理起源的谜题。
• 检验水瀑布是否源于局域电子关联，而非自旋涨落或声子。
• 建立 Hubbard 带的出现与水瀑布状谱特征形成之间的直接联系。
• 使用从第一性原理获得的参数在 Hubbard 模型中验证该机制，并与铜氧化物和镍氧化物的实验 ARPES 数据进行比较。

提出的方法

• 采用动态平均场理论（DMFT）求解基于第一性原理获得参数的二维 Hubbard 模型。
• 通过 Dyson 方程 G(k, ω) = [ω − εk − Σ(ω) + iδ]⁻¹ 跟踪谱函数 A(k, ω)，其中 Σ(ω) 为自能。
• 通过求解极点方程 ω = εk + ReΣ(ω) 的图形解法，识别谱权重变为垂直且展宽的位置。
• 将 DMFT 结果与动态顶点近似（DΓA）进行比较，以评估非局域关联（如自旋涨落）的作用。
• 对模拟的谱函数与空穴掺杂铜氧化物和镍氧化物的实验 ARPES 数据进行直接对比。
• 分析能量分布曲线（EDCs）和动量分布曲线（MDCs），包括其二阶导数，以突出水瀑布特征。

实验结果

研究问题

• RQ1 当局域电子关联导致 Hubbard 带从准粒子带分离时，是否自然产生谱函数中的水瀑布状特征？
• RQ2 在铜氧化物和镍氧化物中观察到的水瀑布是否可以在不引入自旋涨落或声子的情况下得到解释？
• RQ3 在 Hubbard 模型中，水瀑布结构在不同关联强度和掺杂水平下是否具有鲁棒性？
• RQ4 非局域关联（如自旋涨落）在多大程度上改变了水瀑布结构，而非使其产生？
• RQ5 使用从第一性原理参数的 DMFT 模拟在多大程度上能准确再现关联氧化物中实验 ARPES 谱？

主要发现

• 当 Hubbard 带由于局域电子关联从准粒子带分离时，水瀑布结构自然产生，无需额外引入玻色模式。
• 在 DMFT 模拟中，水瀑布结构在广泛的 Hubbard 关联强度 U 和掺杂范围内均被观察到，解释了其在铜氧化物和镍氧化物中的普遍存在。
• 该机制源于条件 ∂ReΣ(ω)/∂ω = 1，该条件导致能量-动量平面中谱权重垂直且强烈展宽。
• 即使通过 DΓA 引入非局域关联，水瀑布依然存在，且起源于局域关联，证实了 DMFT 的核心作用。
• 使用从第一性原理参数的模拟谱函数与铜氧化物和镍氧化物的实验 ARPES 数据表现出极佳的定量一致性。
• 水瀑布并非矩阵元效应，这一点已通过该特征在不同关联处理下的鲁棒性以及其与自能频率导数的直接关联得到证实。