Holographic quantum matter

TL;DR

This review surveys holographic approaches to quantum matter without quasiparticles, outlining how gravity in higher dimensions encodes the non-perturbative dynamics of strongly coupled boundary states. It lays out the essential AdS/CMT dictionary, Wilsonian holographic renormalization, and entanglement geometry, establishing how bulk horizons govern dissipation and transport. The text then develops zero-density and finite-density holographic fixed points, including Lifshitz and hyperscaling-violating geometries, AdS2 IR limits, and compressed phases with charged horizons, and discusses spectral functions, diffusion, and the role of quasinormal modes as the competitive excitations replacing quasiparticles. A major theme is the dichotomy between cohesive and fractionalized charge, Fermi-surface signatures in holography, and the rich array of non-quasiparticle transport phenomena that emerge in both zero and finite density holographic matter. The work further connects holographic results to condensed-matter phenomena such as strange metals, quantum critical transport, and emergent gauge fields, highlighting both the explanatory power and current limitations of holographic models for real materials.

Abstract

We present a review of theories of states of quantum matter without quasiparticle excitations. Solvable examples of such states are provided through a holographic duality with gravitational theories in an emergent spatial dimension. We review the duality between gravitational backgrounds and the various states of quantum matter which live on the boundary. We then describe quantum matter at a fixed commensurate density (often described by conformal field theories), and also compressible quantum matter with variable density, providing an extensive discussion of transport in both cases. We present a unified discussion of the holographic theory of transport with memory matrix and hydrodynamic methods, allowing a direct connection to experimentally realized quantum matter. We also explore other important challenges in non-quasiparticle physics, including symmetry broken phases such as superconductors and non-equilibrium dynamics.

Figures (43)

• Figure 1: Low energy excitations of a stack of D3 branes at weak and strong 't Hooft coupling. Weak coupling: $N^2$ light string states connecting the $N$ D3 branes. Strong coupling: classical gravitational excitations that are strongly redshifted by an event horizon.
• Figure 2: Essential dictionary: The boundary value $h$ of a bulk field $\phi$ is a source for an operator ${\mathcal{O}}$ in the dual QFT.
• Figure 3: The radial direction: Events in the interior of the bulk capture long distance, low energy dynamics of the dual field theory. Events near the boundary of the bulk describe short distance, UV dynamics in the field theory dual. The simplest way to think about this is that the interior events are increasingly redshifted relative to the boundary energy scales (a similar logic was used in the decoupling argument of § \ref{['sec:malda']} to derive holographic duality, here we are discussing redshifts within the near horizon AdS region itself).
• Figure 4: The Wilsonian cutoff: The cutoff is at $r=\epsilon$, while the UV fixed point theory is at $r=0$. The partition function $Z^\epsilon[\phi^\epsilon]$ is over all modes at $r > \epsilon$, subject to the boundary condition $\phi(\epsilon) = \phi^\epsilon$. The partition function $Z^\epsilon_\text{UV}[\phi^\epsilon,h]$ is over all modes between $r=\epsilon$ and $r=0$, with boundary conditions at both ends.
• Figure 5: Minimal surface$\Gamma$ in the bulk, whose area gives the entanglement entropy of the region $A$ on the boundary.