Spread complexity rate as proper momentum

We demonstrate a precise relation between the rate of complexity of quantum states excited by local operators in two-dimensional conformal field theories and the radial momentum of particles in three-dimensional anti–de Sitter spacetimes. Similar relations have been anticipated based on qualitative models for operator growth. Here, we make this correspondence sharp with two key ingredients: the precise definition of quantum complexity given by the spread complexity of states, and the match of its growth rate to the bulk momentum measured in the proper radial distance coordinate.

• EC
  European Commission

  Award: 101125449
• NN
  National Natural Science Foundation of China

  Award: 12175238
• NC
  Narodowe Centrum Nauki

  Award: 9 2019/34/E/ST2/00123
• EA
  Engineering and Physical Sciences Research Council
• SA
  Science and Technology Facilities Council

  Award: ST/X000494/1
• ER
  European Research Council

  Award: 101125449