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Spread complexity rate as proper momentum

Year: 2026
Type: article
Abstract: 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.
DOI: 10.1103/7zs8-9zpg
Authors: Pawel Caputa, Bowen Chen, Ross W. McDonald, Joan Simón, Benjamin Strittmatter
Institutions: Stockholm University, Kyoto University, Yukawa Institute for Theoretical Physics, University of Warsaw, Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, University of Edinburgh
Language: English
Open Access status: hybrid
Funders: European Commission, National Natural Science Foundation of China, Narodowe Centrum Nauki, Engineering and Physical Sciences Research Council, Science and Technology Facilities Council, European Research Council
OpenAlex ID: W4404346398
FWCI: 40.67
Cites: 85
Cited by: 14
Related to: 10