Fast holographic inversion of superconducting domes
Sejin Kim
原文摘要
A holographic superconductor whose scalar mass depends on the gauge field strength, $M(\Fsq)$, reproduces a superconducting dome for a suitable $M$, but recovering $M$ from a dome has taken days. We obtain the condition that fixes the critical temperature from two integrations, started at the horizon and at the boundary, and its derivative with respect to $M$ from the same two solutions, so training needs no finite differences and an inversion takes ten minutes to an hour. With this speed we study the interval between the horizon value of $\Fsq$ at the lowest doping and $\Fsq=0$, which no horizon reaches and at whose end the scalar mass $M(0)$ fixes the dimension of the dual operator. Holding $M(0)$ at several values, the pinned masses, and retraining the rest, we find reconstructions that share the minima of $M$ and agree wherever the horizons reach, apart from the deepest end, but differ on that interval. A rule that keeps the reconstruction with the simplest closed form recovers the scalar mass and the mass function of a dome generated from a quadratic $M$. On Gaussian and double-Gaussian domes and the measured phase diagrams of YBa$_{2}$Cu$_{3}$O$_{y}$ and 2M-WS$_{2}$ its choice rests on ties or narrow margins, and it recovers the scalar mass of only two of the four domes generated from the closed forms it keeps for them. The dome thus constrains $M$ where its horizons reach but not the scalar mass, which a second observable would have to fix.
hep-th · cs.AI