Holographic model for the anomalous scalings of the cuprates

TL;DR

This paper presents a holographic model using nonlinear DBI dynamics and hyperscaling-violating geometries to replicate the anomalous temperature-dependent transport properties of cuprate strange metals, highlighting the role of nonlinear interactions.

Contribution

It introduces a holographic framework with nonlinear DBI action and hyperscaling violation to explain anomalous transport in cuprates, emphasizing the impact of nonlinear dynamics.

Findings

Reproduces linear resistivity and quadratic Hall angle temperature dependence.

Supports a wide spectrum of temperature scalings due to nonlinear DBI interactions.

Provides analytical backreacted solutions illustrating different relaxation times.

Abstract

We examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the nonlinear Dirac-Born-Infeld (DBI) action. Axionic scalar fields are included to break translational invariance and generate momentum dissipation in the system. Scaling exponents are introduced by using geometries which are nonrelativistic and hyperscaling-violating in the infrared. In the probe DBI limit the theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals, $\rho \sim T$ and $\cot\Theta_H \sim T^2$. These scaling laws would not be present without the nonlinear dynamics encoded by the DBI interactions. We further show that because of its richness the DBI theory supports a wide spectrum of temperature scalings. This model provides explicit examples in which transport is controlled by different relaxation times. On the other hand, when only one quantity sets the temperature scale of the system, the Hall angle and conductivity typically exhibit the same temperature behavior. We illustrate this point using new fully backreacted analytical dyonic black brane solutions.