Strange metals and the AdS/CFT correspondence

TL;DR

The work links strange-metal behavior to AdS/CFT by connecting quantum impurity problems in a CFT3 to self-consistent lattice Kondo models. It identifies an AdS2 × R^{D-1} holographic metal as the low-energy description of a fractionalized Fermi liquid (FL*) and demonstrates, via large-N impurity analysis, conformal Green's functions and nontrivial impurity entropy consistent with holographic expectations. The study argues that holographic strange metals and FL* states share essential non-Fermi-liquid features while noting the need to incorporate emergent gauge fields to capture full spin-liquid physics and spatial correlations. Together, these results offer a unified framework linking condensed-matter quantum criticality, impurity physics, and holography for strange metals, and point to avenues for refining holographic models to include gauge dynamics and realistic spin liquids.

Abstract

I begin with a review of quantum impurity models in condensed matter physics, in which a localized spin degree of freedom is coupled to an interacting conformal field theory in d = 2 spatial dimensions. Their properties are similar to those of supersymmetric generalizations which can be solved by the AdS/CFT correspondence; the low energy limit of the latter models is described by a AdS2 geometry. Then I turn to Kondo lattice models, which can be described by a mean- field theory obtained by a mapping to a quantum impurity coupled to a self-consistent environment. Such a theory yields a 'fractionalized Fermi liquid' phase of conduction electrons coupled to a critical spin liquid state, and is an attractive mean-field theory of strange metals. The recent holographic description of strange metals with a AdS2 x R2 geometry is argued to be related to such mean-field solutions of Kondo lattice models.

Figures (4)

• Figure 1: The dimer antiferromagnet. The full red lines represent an exchange interaction $J$, while the dashed green lines have exchange $J/g$. The ellispes represent a singlet valence bond of spins $(|\uparrow \downarrow \rangle - | \downarrow \uparrow \rangle )/\sqrt{2}$.
• Figure 2: A frustrated square lattice antiferromagnet on the square lattice, with the Hamiltonian preserving the full space group symmetry of the square lattice. The valence bond solid (VBS) state for $g>g_c$ is four-fold degenerate, depending upon the crystallization pattern of the singlet valence bonds.
• Figure 3: A quantum spin coupled via an exchange interaction to a CFT in 2+1 dimensions.
• Figure 4: The rainbow graphs. The full line is the fermion, and double-dashed line is the interaction $D(\tau)$. Each line, full or dashed, carries a SU($N$) index $\alpha$.