Further studies on holographic insulator/superconductor phase transitions from Sturm-Liouville eigenvalue problems

TL;DR

This paper uses Sturm-Liouville eigenvalue problems to analytically study holographic insulator/superconductor phase transitions, accurately estimating multiple stable modes and improving boundary condition assumptions.

Contribution

It introduces a novel analytical approach that estimates multiple stable modes and relaxes boundary condition constraints, enhancing precision in phase transition analysis.

Findings

Analytical method matches numerical results

Estimates multiple stable modes

Relaxed boundary condition improves accuracy

Abstract

We take advantage of the Sturm-Liouville eigenvalue problem to analytically study the holographic insulator/superconductor phase transition in the probe limit. The interesting point is that this analytical method can not only estimate the most stable mode of the phase transition, but also the second stable mode. We find that this analytical method perfectly matches with other numerical methods, such as the shooting method. Besides, we argue that only Dirichlet boundary condition of the trial function is enough under certain circumstances, which will lead to a more precise estimation. This relaxation for the boundary condition of the trial function is first observed in this paper as far as we know.