Operator K-complexity in DSSYK: Krylov complexity equals bulk length

Article Article scientifique Article Operator K-complexity in DSSYK: Krylov complexity equals bulk length eng 2025-08-07 2025 author Ambrosini Marco Geneva U., Dept. Theor. Phys. 411786 Département de physique théorique (FITEO) author Rabinovici Eliezer Hebrew U. author Sánchez-Garrido Adrián Southampton U. author Shir Ruth Luxembourg U. author Sonner Julian Geneva U., Dept. Theor. Phys. 843498 Département de physique théorique (FITEO) 10.1007/jhep08(2025)059 1029-8479 2412.15318 https://link.springer.com/10.1007/JHEP08(2025)059 In this paper we study the notion of complexity under time evolution in chaotic quantum systems with holographic duals. Continuing on from our previous work, we turn our attention to the issue of Krylov complexity upon the insertion of a class of single-particle operators in the double-scaled SYK model. Such an operator is described by a matter-chord insertion, which splits the theory into left/right sectors, allowing us, via chord-diagram technology, to compute two different notions of complexity associated to the operator insertion: first a Krylov operator complexity, and second the Krylov complexity of a state obtained by an operator acting on the thermofield double state. We will provide both an analytic proof and detailed numerical evidence, that both Krylov complexities arise from a recursively defined basis of states characterized by a constant total chord number. As a consequence, in all cases we are able to establish that Krylov complexity is given by the expectation value of a length operator acting on the Hilbert space of the theory, expressed in terms of basis states, organized by left and right chord number. We find analytic expressions for the semiclassical limit of K-complexity, and study how the size of the operator encodes the scrambling dynamics upon the matter insertion in Krylov language. We furthermore determine the effective Hamiltonian governing the evolution of K-complexity, showing that evolution on the Krylov chain can equivalently be understood as a particle moving in a Morse potential. A particular type of triple scaling limit allows to access the gravitational sector of the theory, in which the geometrical nature of K-complexity is assured by virtue of being a total chord length, in an analogous fashion to what was found in [1] for the K-complexity of the thermofield double state. 2D Gravity AdS-CFT Correspondence Black Holes Field Theories in Lower Dimensions Dewey 500.2 37 Département de physique théorique 133 false The journal of high energy physics 08 8 acb3bfeb-be04-4a5a-96d9-464d56637b11 Article (Published version) Public Article_scientifique_from_unpaywall.pdf 2736148 application/pdf CC BY-4.0 ba1af76c578fa2dc97e7603cb07e760fb0f799fe0f32bbca122a4ff6e7f7a69f openAccess Faculté des sciences / Section de physique / Département de physique théorique

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Operator K-complexity in DSSYK: Krylov complexity equals bulk length	The journal of high energy physics			2025	14	22

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Ambrosini, Marco