{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:34:18Z","timestamp":1760146458546,"version":"build-2065373602"},"reference-count":88,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T00:00:00Z","timestamp":1730764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish MCIN with funding from the European Union Next Generation EU","award":["PRTRC17.I1","PID2023-148409NB-I00 MTM"],"award-info":[{"award-number":["PRTRC17.I1","PID2023-148409NB-I00 MTM"]}]},{"name":"Consejer\u00eda de Educaci\u00f3n from Junta de Castilla y Leon through the QCAYLE project","award":["PRTRC17.I1","PID2023-148409NB-I00 MTM"],"award-info":[{"award-number":["PRTRC17.I1","PID2023-148409NB-I00 MTM"]}]},{"name":"AEI\/10.13039\/501100011033","award":["PRTRC17.I1","PID2023-148409NB-I00 MTM"],"award-info":[{"award-number":["PRTRC17.I1","PID2023-148409NB-I00 MTM"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum many-body systems, and has been typically studied in a sudden quench scenario. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution. In particular, we analyze how the symmetry-breaking information of an initial state is scrambled in adiabatically driven integrable systems, such as the Lipkin\u2013Meshkov\u2013Glick and quantum Rabi models. Following a time-dependent protocol that drives the system from symmetry-breaking to a normal phase, we show how the initial information is scrambled, even for perfect adiabatic evolutions, as indicated by the expectation value of a suitable observable. We detail the underlying mechanism for quantum information scrambling, its relation to ground- and excited-state quantum phase transitions, and quantify the degree of scrambling in terms of the number of eigenstates that participate in the encoding of the initial symmetry-breaking information. While the energy of the final state remains unaltered in an adiabatic protocol, the relative phases among eigenstates are scrambled, and so is the symmetry-breaking information. We show that a potential information retrieval, following a time-reversed protocol, is hindered by small perturbations, as indicated by a vanishingly small Loschmidt echo and out-of-time-ordered correlators. The reported phenomenon is amenable for its experimental verification, and may help in the understanding of information scrambling in critical quantum many-body systems.<\/jats:p>","DOI":"10.3390\/e26110951","type":"journal-article","created":{"date-parts":[[2024,11,5]],"date-time":"2024-11-05T11:36:39Z","timestamp":1730806599000},"page":"951","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Information Scrambling in Adiabatically Driven Critical Systems"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1243-0839","authenticated-orcid":false,"given":"Ricardo","family":"Puebla","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Legan\u00e9s, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1855-0671","authenticated-orcid":false,"given":"Fernando J.","family":"G\u00f3mez-Ruiz","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica Te\u00f3rica, At\u00f3mica y \u00d3ptica, Universidad de Valladolid, 47011 Valladolid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"040302","DOI":"10.1103\/PhysRevA.94.040302","article-title":"Measuring the scrambling of quantum information","volume":"94","author":"Swingle","year":"2016","journal-title":"Phys. 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