Quantum many-body physics from a gravitational lens

Abstract

The past two decades have seen the emergence of remarkable interconnections among previously remotely related disciplines, such as condensed matter, nuclear physics, gravity and quantum information, fuelled both by experimental advances and by the new powerful theoretical methods offered by holographic duality. In this 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 the 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 to demonstrate the unitarity of black hole evaporation.

Key points

  • Holographic duality is an equivalence relation between a gravitational theory in d + 1 dimensions and ordinary quantum systems in d dimensions.

  • The duality provides powerful analytical and numerical approaches to study properties of strongly correlated quantum systems without quasiparticles in otherwise inaccessible regimes.

  • Holographic duality gives new insights into equilibrium and non-equilibrium properties of strange metallic phases, and leads to new conceptual and technical breakthroughs in the study of quantum chaos.

  • The duality reveals deep connections between quantum information and geometry, which in turn lead to new understanding of propagation of quantum information and the structure of spacetime itself.

  • Combining ideas from holography and quantum information theory results in innovative approaches to the long-standing question of whether a black hole destroys information.

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Fig. 1: Minimal surface γA for the Ryu–Takayanagi formula in equation (6).
Fig. 2: Geometric features of gapped and gapless systems.
Fig. 3: Similar roles played by the SLQL phase and the strange metal phase of cuprates in their respective phase diagrams.
Fig. 4: A cartoon visualization of the scrambling phenomenon.
Fig. 5: The phenomenon of ‘pole skipping’ in the energy–energy correlation function.
Fig. 6: Phenomenon of regenesis and its gravity interpretation.
Fig. 7: Quantum information and geometry.

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Acknowledgements

The authors thank N. Engelhardt, D. Harlow, A. Krikun, J. Minahan and J. Zaanen for discussions. This work is supported by the Office of High Energy Physics of the US Department of Energy under grant contract number DE-SC0012567. This work has also been supported by the Fonds National Suisse de la Recherche Scientifique (Schweizerischer Nationalfonds zur Förderung der wissenschaftlichen Forschung) through project grants 200021_162796 and 200020_182513 as well as the NCCR 51NF40-141869 The Mathematics of Physics (SwissMAP).

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Liu, H., Sonner, J. Quantum many-body physics from a gravitational lens. Nat Rev Phys 2, 615–633 (2020). https://doi.org/10.1038/s42254-020-0225-1

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