Towards strange metallic holography (0912.1061v2)

Abstract: We initiate a holographic model building approach to `strange metallic' phenomenology. Our model couples a neutral Lifshitz-invariant quantum critical theory, dual to a bulk gravitational background, to a finite density of gapped probe charge carriers, dually described by D-branes. In the physical regime of temperature much lower than the charge density and gap, we exhibit anomalous scalings of the temperature and frequency dependent conductivity. Choosing the dynamical critical exponent $z$ appropriately we can match the non-Fermi liquid scalings, such as linear resistivity, observed in strange metal regimes. As part of our investigation we outline three distinct string theory realizations of Lifshitz geometries: from F theory, from polarised branes, and from a gravitating charged Fermi gas. We also identify general features of renormalisation group flow in Lifshitz theories, such as the appearance of relevant charge-charge interactions when $z \geq 2$. We outline a program to extend this model building approach to other anomalous observables of interest such as the Hall conductivity.

• The paper develops a holographic model coupling a Lifshitz-invariant theory with probe D-branes to replicate strange metals' linear resistivity.
• It rigorously explores critical scaling laws by tuning the dynamic exponent, reproducing key non-Fermi liquid behaviors.
• The study analyzes DC, Hall, and AC conductivities, highlighting deviations from classical predictions in strange metal transport.

Towards Strange Metallic Holography: An Overview

The paper "Towards Strange Metallic Holography" by Hartnoll, Polchinski, Silverstein, and Tong develops a holographic framework intended to model the properties of 'strange metals'. These materials exhibit unusual electronic behaviors that traditional theoretical frameworks struggle to explain, notably including linear resistivity over a broad temperature range. This research aims to elucidate these phenomena through the lens of gauge/gravity duality, advancing the understanding of non-Fermi liquid behaviors.

Key Components and Methodology

1. Holographic Model Structure: The authors construct a model coupling a neutral Lifshitz-invariant quantum critical theory with a finite density of charged carriers. These carriers are treated as probe D-branes within a bulk geometric framework. This setup allows for the exploration of anomalous electric transport characteristics observed in strange metals.
2. Critical Scaling Analysis: By tuning the dynamic critical exponent $z$, the model reproduces key non-Fermi liquid features. Specifically, for $z=2$, linear resistivity with temperature is achieved—a haLLMark of strange metallic behavior. The implications of various $z$ values are rigorously explored, providing insights into critical scaling laws.
3. Conductivity Investigations: The paper thoroughly analyzes DC, Hall, and AC conductivities using this holographic model. A prominent finding is that the resistivity scales linearly with temperature when the charge density dominates, aligning with strange metal observations. The authors also explore the effects of an external magnetic field, noting deviations from classical Drude predictions, particularly in the Hall conductivity.
4. String Theory Realizations: The paper outlines three distinct realizations for Lifshitz geometries derived from string theory — via F theory, polarized branes, and gravitating charged fermionic systems. These realizations ensure the theoretical robustness and UV-complete nature of the proposed Lifshitz models.

Results Summary

• Thermodynamics and Transport Properties: The paper highlights the scaling dimensions of various observables, predicting specific heat and susceptibility behaviors under the scaling hypothesis.
• Nontrivial Exponents: The paper identifies specific regimes where the conductivity demonstrates nontrivial power-law frequency dependencies.

Implications and Future Directions

The theoretical construct opens pathways to potentially replicating other strange metal phenomena, like anomalous Hall conductivity, within the holographic framework. It suggests that a similar approach could be applied to the high-temperature superconductors and heavy fermion compounds experiencing similar quantum critical dynamics.

Upon examining string theory settings, the authors propose potential correlations between the critical exponents in their models and those observed experimentally in other real-world strange metals. This highlights an avenue for further paper into the viability of these models to predict novel, tangible material behaviors.

Conclusion

This paper is a substantial exploration into using holographic duality to model and possibly understand phenomena associated with strange metals, specifically their unconventional electron transport properties. By establishing a correlation between high-energy physics models and condensed matter theory, the authors not only contribute to theoretical physics but potentially pave the way for new insights into material science. The work is a promising step towards a deeper understanding of non-Fermi liquid behaviors and their underlying physical mechanisms, capable of extending the predictive capacity of theoretical models in novel regimes.