More on complexity of operators in quantum field theory

  • Run-Qiu Yang
  • Yu-Sen An
  • Chao Niu
  • Cheng-Yong Zhang
  • Keun-Young KimEmail author
Open Access
Regular Article - Theoretical Physics


Recently it has been shown that the complexity of SU(n) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten p-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as k-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU(n) groups.


Gauge-gravity correspondence Holography and condensed matter physics (AdS/CMT) 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Run-Qiu Yang
    • 1
  • Yu-Sen An
    • 2
    • 3
  • Chao Niu
    • 4
  • Cheng-Yong Zhang
    • 5
  • Keun-Young Kim
    • 6
    Email author
  1. 1.Quantum Universe CenterKorea Institute for Advanced StudySeoulKorea
  2. 2.Key Laboratory of Theoretical Physics, Institute of Theoretical PhysicsChinese Academy of ScienceBeijingChina
  3. 3.School of physical ScienceUniversity of Chinese Academy of ScienceBeijingChina
  4. 4.Department of Physics and Siyuan LaboratoryJinan UniversityGuangzhouChina
  5. 5.Department of Physics and Center for Field Theory and Particle PhysicsFudan UniversityShanghaiChina
  6. 6.School of Physics and ChemistryGwangju Institute of Science and TechnologyGwangjuKorea

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