AI 中文总结
基于神经常微分方程开发数据驱动框架，从边界费米子谱函数学习静态平面对称黑洞的整体度规函数和\(U(1)\)规范势，验证后用于铜酸盐奇异金属相，分析其适用性边界。
AI 中文摘要
我们基于神经常微分方程开发了一个数据驱动框架，该框架从边界费米子谱函数中学习静态、平面对称黑洞的整体度规函数和\(U(1)\)规范势。在以高精度验证爱因斯坦 - 麦克斯韦和古布泽 - 罗查模型上的框架后，我们将其应用于半全息环境下的铜酸盐\((Pb,Bi)_2Sr_{2 - x}La_xCuO_{6 + \delta}\)的奇异金属相，将通过角分辨光电子能谱测量校准的扩展幂律液体（PLL）模型生成的光谱数据作为输入。在低温和近最佳掺杂情况下，我们表明归一化的扩展PLL模型可以由具有几乎消失的规范势（\(qA_t\sim10^{-4}\,\mathrm{eV}\)）的\(\mathrm{AdS}_{2}\times\mathbb{R}^{2}\)黑洞附近共形类的有效代表很好地描述。一个关键的结构观察是我们的探测费米子是无质量的，因此对共形因子\(\Omega(z)\)不敏感。这进一步意味着固定宏观热力学，如电子比热，将需要超出费米子谱的独立输入。我们还描绘了我们框架的适用性边界：学习到的有效模型在低温下的整个掺杂范围内仍然可行，随着样品从边缘费米液体点向过掺杂侧移动，损失略有增加；主要限制是温度，损失和\(qA_t\)都会大幅增长。
英文摘要
We develop a data-driven framework based on Neural ODEs that learns the effective bulk metric functions and the charge-weighted gauge potential $qA_t$ of a static, planar-symmetric black hole from boundary fermionic spectral functions. After validating the framework on the Einstein--Maxwell and Gubser--Rocha models with high accuracy, we apply it to the nodal strange-metal phenomenology of the cuprate $\mathrm{(Pb,Bi)_2Sr_{2-x}La_xCuO_{6+δ}}$ within a semi-holographic setting, taking as input the normalized target generated from the extended power-law liquid (PLL) model calibrated by angle-resolved photoemission measurements. A key structural observation is that our probe fermion is massless and therefore insensitive to the conformal factor, leading to a coordinate/Weyl redundancy, while spectral normalization introduces a degeneracy in the scaled Hawking temperature. After identifying these sources of nonuniqueness, we find that, at low temperatures and near-optimal doping, the normalized extended-PLL target can be well described by a family of effective geometries close to the conformal-to-$\mathrm{AdS}_{2}\times\mathbb{R}^{2}$ black-hole class, with a nearly vanishing $qA_t$ ($\sim10^{-4}\,\mathrm{eV}$). The conformal-factor ambiguity further implies that fixing macroscopic thermodynamics such as the electronic specific heat requires independent input beyond the fermionic spectra. We also examine the applicability of our framework across doping and temperature: at low temperatures, the learned effective model remains viable throughout the studied doping range, with only a mild increase in loss toward the overdoped side; at higher temperatures, however, both the loss and $qA_t$ increase substantially.
Comments43 pages, 10 figures, 4 tables
