Stanford Advisors


All Publications


  • A symmetry algebra in double-scaled SYK SCIPOST PHYSICS Lin, H. W., Stanford, D. 2023; 15 (6)
  • Universality in long-distance geometry and quantum complexity. Nature Brown, A. R., Freedman, M. H., Lin, H. W., Susskind, L. 2023; 622 (7981): 58-62

    Abstract

    In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class1. Here we apply this viewpoint to geometry and initiate a program of classifying homogeneous metrics on group manifolds2 by their long-distance properties. We show that many metrics on low-dimensional Lie groups have markedly different short-distance properties but nearly identical distance functions at long distances, and provide evidence that this phenomenon is even more robust in high dimensions. An application of these ideas of particular interest to physics and computer science is complexity geometry3-7-the study of quantum computational complexity using Riemannian geometry. We argue for the existence of a large universality class of definitions of quantum complexity, each linearly related to the other, a much finer-grained equivalence than typically considered. We conjecture that a new effective metric emerges at larger complexities that describes a broad class of complexity geometries, insensitive to various choices of microscopic penalty factors. We discuss the implications for recent conjectures in quantum gravity.

    View details for DOI 10.1038/s41586-023-06460-3

    View details for PubMedID 37794268

    View details for PubMedCentralID 3763255

  • Bootstrap bounds on D0-brane quantum mechanics JOURNAL OF HIGH ENERGY PHYSICS Lin, H. W. 2023
  • Quantum Gravity in the Lab. I. Teleportation by Size and Traversable Wormholes PRX QUANTUM Brown, A. R., Gharibyan, H., Leichenauer, S., Lin, H. W., Nezami, S., Salton, G., Susskind, L., Swingle, B., Walter, M. 2023; 4 (1)
  • Quantum Gravity in the Lab. II. Teleportation by Size and Traversable Wormholes PRX QUANTUM Nezami, S., Lin, H. W., Brown, A. R., Gharibyan, H., Leichenauer, S., Salton, G., Susskind, L., Swingle, B., Walter, M. 2023; 4 (1)
  • The bulk Hilbert space of double scaled SYK JOURNAL OF HIGH ENERGY PHYSICS Lin, H. W. 2022
  • The entanglement wedge of unknown couplings JOURNAL OF HIGH ENERGY PHYSICS Almheiri, A., Lin, H. W. 2022
  • Bootstraps to strings: solving random matrix models with positivite JOURNAL OF HIGH ENERGY PHYSICS Lin, H. W. 2020
  • Complexity geometry and Schwarzian dynamics JOURNAL OF HIGH ENERGY PHYSICS Lin, H. W., Susskind, L. 2020
  • Complexity of Jackiw-Teitelboim gravity PHYSICAL REVIEW D Brown, A. R., Gharibyan, H., Lin, H. W., Susskind, L., Thorlacius, L., Zhao, Y. 2019; 99 (4)
  • Why Does Deep and Cheap Learning Work So Well? JOURNAL OF STATISTICAL PHYSICS Lin, H. W., Tegmark, M., Rolnick, D. 2017; 168 (6): 1223-1247