Spread complexity in saddle-dominated scrambling
Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scramb...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/414813 |
| Acceso en línea: | http://hdl.handle.net/10261/414813 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85193639553&doi=10.1007%2FJHEP05%282024%29137&partnerID=40&md5=b92ddd3111abca5d1ee899cd7dac08d2 |
| Access Level: | acceso abierto |
| Palabra clave: | AdS-CFT Correspondence Field Theories in Lower Dimensions Integrable Field Theories |
| Sumario: | Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scrambling. Specifically, we focus on the Lipkin-Meshkov-Glick model and the inverted harmonic oscillator as representative examples of quantum mechanical systems featuring saddle-dominated scrambling. Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of chaotic systems, displaying a distinctive ramp-peak-slope-plateau pattern. Our results indicate that, although spread complexity serves as a valuable probe, accurately diagnosing true quantum chaos generally necessitates additional physical input. We also explore the relationship between spread complexity, the spectral form factor, and the transition probability within the Krylov space. We provide analytical confirmation of our numerical results, validating the Ehrenfest theorem of complexity and identifying a distinct quadratic behavior in the early-time regime of spread complexity. © The Author(s) 2024. |
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