Chaos in the butterfly cone
Abstract A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observe...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)186 |
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| _version_ | 1823863484642754560 |
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| author | Márk Mezei Gábor Sárosi |
| author_facet | Márk Mezei Gábor Sárosi |
| author_sort | Márk Mezei |
| collection | DOAJ |
| description | Abstract A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/vB), where T is the temperature and vB is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v* < vB. In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature. |
| format | Article |
| id | doaj-art-d662c9f40c01414db62fe97ab23372e8 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d662c9f40c01414db62fe97ab23372e82025-02-09T12:06:38ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020113410.1007/JHEP01(2020)186Chaos in the butterfly coneMárk Mezei0Gábor Sárosi1Simons Center for Geometry and Physics, State University of New York (SUNY)David Rittenhouse Laboratory, University of PennsylvaniaAbstract A simple probe of chaos and operator growth in many-body quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − |v|/vB), where T is the temperature and vB is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v* < vB. In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.https://doi.org/10.1007/JHEP01(2020)1861/N ExpansionAdS-CFT CorrespondenceConformal Field TheoryQuantum Dissipative Systems |
| spellingShingle | Márk Mezei Gábor Sárosi Chaos in the butterfly cone Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Quantum Dissipative Systems |
| title | Chaos in the butterfly cone |
| title_full | Chaos in the butterfly cone |
| title_fullStr | Chaos in the butterfly cone |
| title_full_unstemmed | Chaos in the butterfly cone |
| title_short | Chaos in the butterfly cone |
| title_sort | chaos in the butterfly cone |
| topic | 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Quantum Dissipative Systems |
| url | https://doi.org/10.1007/JHEP01(2020)186 |
| work_keys_str_mv | AT markmezei chaosinthebutterflycone AT gaborsarosi chaosinthebutterflycone |