Condensed matter and AdS/CFT

TL;DR

Subir Sachdev surveys two intertwined classes of strong-coupling problems in two-dimensional condensed matter: quantum-critical dynamics near relativistic fixed points and symmetry-breaking transitions in metals with gapless fermions. He shows how AdS/CFT can yield exact real-time transport results in quantum-critical regimes and how hydrodynamics provides a complementary low-frequency description, including cyclotron resonances and universal conductivities. The discussion covers model systems (coupled dimers, deconfined criticality, graphene), fermionic criticality in d-wave superconductors (Dirac fermions, time-reversal breaking, Ising-nematic order), and metallic quantum criticality with Fermi surfaces, highlighting both field-theoretic and holographic approaches. The work emphasizes emergent dimensions, dualities, and universality, offering a bridge between condensed matter phenomena and gravitational holography with implications for experiments in graphene, cuprates, and related systems.

Abstract

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.

Figures (12)

• Figure 1: The coupled dimer antiferromagnet. The full red lines represent an exchange interaction $J$, while the dashed green lines have exchange $J/\lambda$. The ellispes represent a singlet valence bond of spins $(|\uparrow \downarrow \rangle - | \downarrow \uparrow \rangle )/\sqrt{2}$.
• Figure 2: Dirac dispersion spectrum for graphene showing a 'topological' quantum phase transition from a hole Fermi surface for $\mu<0$ to a electron Fermi surface for $\mu > 0$.
• Figure 3: Finite temperature crossovers of the coupled dimer antiferromagnet in Fig. \ref{['fig:ssdimer']}.
• Figure 4: Finite temperature crossovers of graphene as a function of electron density $n$ (which is tuned by $\mu$ in Eq. (\ref{['eq:ssgraph']})) and temperature, $T$. Adapted from Ref. sssheehy.
• Figure 5: Spectral weight of the density correlation function of the SCFT3 with $\mathcal{N}=8$ supersymmetry in the collisionless regime.