Quantum many-body physics from a gravitational lens

TL;DR

This survey highlights how holographic duality connects gravity with quantum many-body dynamics, focusing on strongly correlated systems without quasiparticles. By mapping boundary theories to bulk AdS gravity, it reveals universal transport, chaos, and information-theoretic phenomena through geometric constructs like horizons, minimal surfaces, and entanglement wedges. Key contributions include the identification of a universal intermediate-energy SLQL phase at finite density, the precise realization of maximal chaos and its hydrodynamic consequences, and the development of quantum-information-inspired frameworks (subregion duality, quantum extremal surfaces, islands) that illuminate black-hole information and the Page curve. The work underlines the potential of holography to guide understanding of real materials, non-equilibrium dynamics, and the fundamental structure of spacetime, with implications for both theory and experiment.

Abstract

The last two decades have seen the emergence of stunning interconnections among various previously remotely related disciplines such as condensed matter, nuclear physics, gravity and quantum information, fueled both by experimental advances and new powerful theoretical methods brought by holographic duality. In this non-technical review we sample some recent developments in holographic duality in connection with quantum many-body dynamics. These include insights into strongly correlated phases without quasiparticles and their transport properties, quantum many-body chaos, and scrambling of quantum information. We also discuss recent progress in understanding the structure of holographic duality itself using quantum information, including a "local" version of the duality as well as the quantum error correction interpretation of quantum many-body states with a gravity dual, and how such notions help demonstrate the unitarity of black hole evaporation.

Figures (12)

• Figure 1: In holographic duality, a quantum gravity system defined in a $(d+1)$-dimensional anti-de Sitter spacetime is equivalent to a many-body system defined on its $d$-dimensional boundary. Anti-de Sitter spacetime is a curved spacetime of constant negative curvature. It has a radial direction $z$ which runs from $0$ to $+\infty$, with a $d$-dimensional Minkowski spacetime at each constant value of $z$. $z = 0$ is the boundary of the whole spacetime (often referred to as the "bulk" spacetime) and is where the many-body system is defined. At a heuristic level, the radial direction $z$ in the bulk can be interpreted as corresponding to the size of structures in the boundary many-body system. For example, two objects in the bulk that are identical except for their radial coordinate $z$ correspond in the boundary system to two objects that are identical in all respects except for their size--one can be obtained from the other by magnification. This correspondence, with larger structures on the boundary corresponding to deeper structures in the bulk, is the key to how the boundary system can describe all the physics within the bulk even though it has one dimension less. By analogy, the boundary system is referred to as a "hologram" of the bulk system (since in laser physics a hologram is a two-dimensional representation of a three-dimensional object) and we say that there is a "holographic duality" between the boundary many-body system and the bulk quantum gravity system.
• Figure 2: Black holes and lack of quasiparticles. Local disturbances applied to the boundary systems correspond to excitations of the gravity systems near the boundary. Once generated such excitations rapidly fall towards and are absorbed into the black-hole horizon. From the point of view of the boundary system this means that the disturbances are rapidly dissolved into the 'quantum soup' surrounding them, i.e. before they are able to propagate to any appreciable distances, they have already dissipated. Technically it means that the width of any excitation is so large that it cannot be treated as a long-lived quasiparticle.
• Figure 3: Minimal surface ${{\gamma}}_A$ for the the Ryu-Takayanagi formula \ref{['eq.RTformula']}. The figure shows a single time slice of the bulk spacetime. The spatial region ${\mathfrak a}$ between ${{\gamma}}_A$ and $A$, i.e. $\partial {\mathfrak a} = {{\gamma}}_A \cup A$, is often referred to as the "entanglement wedge" associated with $A$ and will play an important role in Sec. \ref{['sec:QI']}. (More precisely, the entanglement wedge refers to the domain of dependence of ${\mathfrak a}$, but here for language simplicity we will not make this distinction.)
• Figure 4: Geometric features of gapped and gapless systems. (a): the geometry represents the flowing from a UV fixed point to an IR fixed point. The geometry becomes scale invariant and is described by \ref{['eq.poincareadsmetric']} as $z \to 0$ and $z \to \infty$ with different curvature radii $\ell$. The intermediate region between them describes the flow between the two fixed points. (b): the geometry represents an RG flow where the UV fixed point flows to gapped theory in the IR, ending smoothly at a maximum radius $z_*$. Another option is that $z_*$ is a singularity, which then needs to be resolved in order to understand the nature of the ground state.
• Figure 5: Left: The semi-local quantum liquid phase as a universal intermediate energy phase. Many different UV systems flow to it, and at lower temperatures depending on parameters it settles into one of many different possible ground states, such as Fermi liquids (FL), anti-ferromagnets (AFM), and superconductors (SC) among others. This is reminiscent of the phase diagram for hole-doped cuprates, where a cartoon is shown on the Right: materials of different microscopic structures flow to the same strange metal phase and then depending on parameters such as doping go over to a variety of other phases at lower temperatures.