What can gauge-gravity duality teach us about condensed matter physics?

TL;DR

This work surveys how gauge-gravity duality (holography) can illuminate two broad classes of condensed-matter states: conformal quantum matter at quantum critical points and compressible quantum matter with finite zero-temperature compressibility. By mapping strongly coupled field theories to higher-dimensional gravitational theories, it provides a framework to compute long-time, finite-temperature dynamics and transport where traditional methods falter, and demonstrates how holography can reproduce or predict universal transport features such as frequency-dependent conductivities. For conformal quantum matter, the AdS/CFT correspondence offers a gravity dual to strongly coupled CFTs, enabling predictions for σ(ω) and highlighting the role of higher-derivative corrections (gamma) in distinguishing particle-like versus vortex-like transport. For compressible matter, RN-AdS4 and AdS2×R2 geometries yield insights into non-Fermi liquids, Fermi surfaces in holographic contexts, and possible back-reacted, Lifshitz-like or confining phases that align with or challenge conventional condensed-matter classifications. Overall, the holographic approach holds promise for a unified, quantitative description of exotic strongly correlated states, while also presenting open questions about back-reaction, Luttinger constraints, and precise phase mappings to known condensed-matter phases.

Abstract

I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with non-zero temperature dynamics and transport are difficult to answer using conventional field theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality, and discuss the prospects for reliable computation of low frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality, and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly-coupled compressible quantum states.

Figures (15)

• Figure 1: Superfluid (left) and insulating states of bosons with repulsive interactions on a square lattice at $f=1$.
• Figure 1: The triangular lattice
• Figure 2: Phase diagram of the superfluid-insulator transition in two spatial dimensions ($D=3$). The quantum critical point is at $g=g_c$, $T=0$. The dashed lines are crossovers, while the full line is a phase transition at the Kosterlitz-Thouless temperature $T_{KT}>0$.
• Figure 2: The electronic dispersion in Eq. (\ref{['hlattri']}) for $\mu=0$ and $t=1$.
• Figure 3: Excitations of the superfluid and the insulator. The excitations of the superfluid are vortices and anti-vortices, which can be viewed as point-like particles centered at the X. A single particle and single hole excitations of the insulator are shown on the right.