Operator K-complexity in DSSYK: Krylov complexity equals bulk length Article Swipe
Marco Ambrosini
,
Eliezer Rabinovici
,
Adrián Sánchez-Garrido
,
Ruth Shir
,
Julian Sonner
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.15318
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.15318
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.
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Operator (biology)
Mathematics
Discrete mathematics
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Metadata
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- Language
- en
- Landing Page
- http://arxiv.org/abs/2412.15318
- https://arxiv.org/pdf/2412.15318
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4405713912
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4405713912Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2412.15318Digital Object Identifier
- Title
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Operator K-complexity in DSSYK: Krylov complexity equals bulk lengthWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-12-19Full publication date if available
- Authors
-
Marco Ambrosini, Eliezer Rabinovici, Adrián Sánchez-Garrido, Ruth Shir, Julian SonnerList of authors in order
- Landing page
-
https://arxiv.org/abs/2412.15318Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2412.15318Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2412.15318Direct OA link when available
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Operator (biology), Mathematics, Discrete mathematics, Algebra over a field, Pure mathematics, Chemistry, Gene, Repressor, Biochemistry, Transcription factorTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.expressions | 183 |
| abstract_inverted_index.furthermore | 210 |
| abstract_inverted_index.geometrical | 258 |
| abstract_inverted_index.holographic | 17 |
| abstract_inverted_index.recursively | 123 |
| abstract_inverted_index.technology, | 69 |
| abstract_inverted_index.thermofield | 102, 287 |
| abstract_inverted_index.K-complexity | 261, 284 |
| abstract_inverted_index.complexities | 119 |
| abstract_inverted_index.consequence, | 137 |
| abstract_inverted_index.equivalently | 228 |
| abstract_inverted_index.matter-chord | 56 |
| abstract_inverted_index.K-complexity, | 189, 219 |
| abstract_inverted_index.characterized | 128 |
| abstract_inverted_index.chord-diagram | 68 |
| abstract_inverted_index.double-scaled | 46 |
| abstract_inverted_index.gravitational | 250 |
| abstract_inverted_index.semiclassical | 186 |
| abstract_inverted_index.single-particle | 42 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile |