发表机构
Korea Institute for Advanced Study（韩国高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种快速全息反演方法，将超导圆顶恢复标量质量函数的时间从数天缩短至十分钟到一小时，并揭示圆顶仅能约束视界所及区域的 $M$，固定对偶算子维度需额外观测量。
AI 中文摘要
一个标量质量依赖于规范场强度 $M(\Fsq)$ 的全息超导体，在合适的 $M$ 下能够重现超导圆顶，而此前从给定的圆顶恢复该 $M$ 需要数天的单次训练时间。我们提出了一种训练该模型的新方法，使得一次反演仅需约十分钟到一小时。训练需要固定临界温度的条件梯度，先前的方法通过有限差分获得该梯度，并对每个训练参数重复体积分。这里，该条件无需任何拟合，通过从视界和边界出发的两次积分获得，其对 $M$ 的导数是同一两个解的积分，因此梯度无需额外的积分。我们利用这一速度研究圆顶无法确定的 $M$ 部分，即在最低掺杂下视界处 $\Fsq$ 的值与 $\Fsq=0$ 之间的区间，其中 $M$ 为标量质量 $M(0)$，它固定了对偶算子的维度。我们将标量质量固定在多个值（称为钉扎质量），每次重新训练其余部分，发现重建在圆顶视界所达到的所有地方（包括 $M$ 的最小值）一致，仅在该区间内不同。一个保持最简闭合形式重建的规则能够恢复测试圆顶的标量质量和质量函数。然而，在高斯和双高斯圆顶以及 YBa$_{2}$Cu$_{3}$O$_{y}$ 和 2M-WS$_{2}$ 的实测相图上，其保留的钉扎质量基于平局或微弱优势，因此对于这些目标，标量质量仍是开放的。因此，圆顶在视界所及之处约束 $M$，而固定对偶算子维度需要第二个观测量。
英文摘要
A holographic superconductor whose scalar mass depends on the gauge field strength, $M(\Fsq)$, reproduces a superconducting dome for a suitable $M$, and recovering that $M$ from a given dome has so far taken days for a single training run. We propose a new way of training this model, with which an inversion takes from about ten minutes to an hour. Training needs the gradient of the condition that fixes the critical temperature, which the earlier method obtains by finite differences, repeating the bulk integrations for every training parameter. Here that condition is obtained, without any fit, from two integrations started at the horizon and at the boundary, and its derivative with respect to $M$ is an integral over the same two solutions, so the gradient needs no integration of its own. We use the speed to study the part of $M$ that a dome cannot determine, on the interval between the value $\Fsq$ takes at the horizon for the lowest doping and $\Fsq=0$, at which $M$ is the scalar mass $M(0)$ that fixes the dimension of the dual operator. We hold the scalar mass at several values, which we call pinned masses, retrain everything else at each, and find that the reconstructions agree wherever the horizons of the dome reach, including the minima of $M$, and differ only on that interval. A rule that keeps the reconstruction with the simplest closed form recovers both the scalar mass and the mass function of a test dome. On Gaussian and double-Gaussian domes and on the measured phase diagrams of YBa$_{2}$Cu$_{3}$O$_{y}$ and 2M-WS$_{2}$, however, the pinned mass it keeps rests on ties or on narrow margins, so for these targets the scalar mass is left open. The dome thus constrains $M$ where its horizons reach, and fixing the dimension of the dual operator needs a second observable.
Comments25 pages, 4 figures
