Effective Holographic Theories for low-temperature condensed matter systems

TL;DR

This work develops and analyzes Effective Holographic Theories (EHTs) for low-temperature condensed matter systems by treating Einstein-Maxwell-Dilaton dynamics with a Liouville-type potential, parameterized by two IR exponents γ and δ. It maps how IR data control the full phase structure, spectra, and transport, including regions with linear-in-T DC resistivity, various AC conductivity scalings, and the emergence of Mott-like insulating behavior in the γδ=1 and γ=δ families, while ensuring IR solutions can be embedded in asymptotically AdS completions. The paper provides extensive analytic and semi-analytic results for zero and finite density, backreacted geometries, near-extremal scaling laws, and transport coefficients, with explicit analyses of spin-2 and current fluctuations, as well as DBI versus Maxwell dynamics. Overall, the findings offer a coherent holographic framework to identify universality classes and transport fingerprints (e.g., σ(ω)∼ω^n and ρ∼T) relevant to strange metals, while highlighting the importance of IR singularities, UV completions, and phase transitions in constraining holographic descriptions of condensed matter systems.

Abstract

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(γ,δ)$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(γ,δ)$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $γ=δ$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(γ,δ)$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

Figures (44)

• Figure 1: Superpotential on (a) the $W_-$ branch and (b) the $W_+$ branch, close to a critical point. The black area is the "forbidden" region below the critical curve $\sqrt{{4(p-1)\over p} V}$, where $W'$ would become imaginary. The solution stops where it meets the critical curve.
• Figure 3: The region allowed on the $\gamma-\delta$ plane from the spin-two and spin-one spectra is displayed in blue for p=3 and p=4 dimensions.
• Figure 4: Temperature as a function of the value of $\lambda$ at the horizon, $\lambda_h$ for the three different cases discussed in the text. Black holes exist only above $T_{min}$ whose precise value depend on the particular zero-$T$ geometry.
• Figure 5: $T$ as a function of $\lambda_h$ in a case with more than two black hole solutions.
• Figure 6: The free energy $F(T)$ for the case of Fig.\ref{['f2']} with multiple extrema. $S_1$ and $S_2$ denote small BHs whereas $B_1$ and $B_2$ denote big BHs. The arrows represent direction of increasing $\lambda_h$. There are two first order phase transitions in this case.