Towards a Holographic Realization of Homes' Law

TL;DR

This paper explores the holographic modeling of Homes' law in strongly correlated quantum systems, analyzing superconductor models to identify universal relations and progress towards a holographic realization of this law.

Contribution

It demonstrates the emergence of Homes' law in holographic superconductor models without backreaction and discusses future steps for more general holographic realizations.

Findings

Homes' law holds in holographic s-wave and p-wave superconductors without backreaction.

Progress made in understanding diffusive processes in holographic models.

Suggestions for extending the holographic realization of Homes' law with backreaction.

Abstract

Gauge/gravity duality has proved to be a very successful tool for describing strongly coupled systems in particle physics and heavy ion physics. The application of the gauge/gravity duality to quantum matter is a promising candidate to explain questions concerning non-zero temperature dynamics and transport coefficients. To a large extent, the success of applications of gauge/gravity duality to the quark-gluon plasma is founded on the derivation of a universal result, the famous ratio of shear viscosity and entropy density. As a base for applications to condensed matter physics, it is highly desirable to have a similar universal relation in this context as well. A candidate for such a universal law is given by Homes' law: High Tc superconductors, as well as some conventional superconductors, exhibit a universal scaling relation between the superfluid density at zero temperature and the conductivity at the critical temperature times the critical temperature itself. In this work we describe progress in employing the models of holographic superconductors to realize Homes' law and to find a universal relation governing strongly correlated quantum matter. We calculate diffusive processes, including the backreaction of the gravitational matter fields on the geometry. We consider both holographic s-wave and p-wave superconductors. We show that a particular form of Homes' law holds in the absence of backreaction. Moreover, we suggest further steps to be taken for holographically realizing Homes' law more generally in the presence of backreaction.