Diagnosing quantum chaos in many-body systems using entanglement as a resource
Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial states. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.013254 |
| _version_ | 1797211570860720128 |
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| author | Étienne Lantagne-Hurtubise Stephan Plugge Oguzhan Can Marcel Franz |
| author_facet | Étienne Lantagne-Hurtubise Stephan Plugge Oguzhan Can Marcel Franz |
| author_sort | Étienne Lantagne-Hurtubise |
| collection | DOAJ |
| description | Classical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial states. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however, in most interacting many-body systems, this is not a viable option. Here we propose a family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of the system. We show that, remarkably, in this situation the Lyapunov chaos exponent λ_{L} can be extracted from the measurement of an ordinary two-point correlation function. As an unexpected bonus, we find that our proposed method yields the so-called “regularized” OTOC—a quantity that is believed to most directly indicate quantum chaos. According to recent theoretical work, the TFD state can be prepared as the ground state of two weakly coupled identical systems and is therefore amenable to experimental study. We illustrate the utility of these protocols on the example of the maximally chaotic Sachdev-Ye-Kitaev model and support our findings by extensive numerical simulations. |
| first_indexed | 2024-04-24T10:28:36Z |
| format | Article |
| id | doaj.art-dfc740a6e27d4f548d3b9e6c0f34119d |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:28:36Z |
| publishDate | 2020-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-dfc740a6e27d4f548d3b9e6c0f34119d2024-04-12T16:50:53ZengAmerican Physical SocietyPhysical Review Research2643-15642020-03-012101325410.1103/PhysRevResearch.2.013254Diagnosing quantum chaos in many-body systems using entanglement as a resourceÉtienne Lantagne-HurtubiseStephan PluggeOguzhan CanMarcel FranzClassical chaotic systems exhibit exponentially diverging trajectories due to small differences in their initial states. The analogous diagnostic in quantum many-body systems is an exponential growth of out-of-time-ordered correlation functions (OTOCs). These quantities can be computed for various models, but their experimental study requires the ability to evolve quantum states backward in time, similar to the canonical Loschmidt echo measurement. In some simple systems, backward time evolution can be achieved by reversing the sign of the Hamiltonian; however, in most interacting many-body systems, this is not a viable option. Here we propose a family of protocols for OTOC measurement that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of the system. We show that, remarkably, in this situation the Lyapunov chaos exponent λ_{L} can be extracted from the measurement of an ordinary two-point correlation function. As an unexpected bonus, we find that our proposed method yields the so-called “regularized” OTOC—a quantity that is believed to most directly indicate quantum chaos. According to recent theoretical work, the TFD state can be prepared as the ground state of two weakly coupled identical systems and is therefore amenable to experimental study. We illustrate the utility of these protocols on the example of the maximally chaotic Sachdev-Ye-Kitaev model and support our findings by extensive numerical simulations.http://doi.org/10.1103/PhysRevResearch.2.013254 |
| spellingShingle | Étienne Lantagne-Hurtubise Stephan Plugge Oguzhan Can Marcel Franz Diagnosing quantum chaos in many-body systems using entanglement as a resource Physical Review Research |
| title | Diagnosing quantum chaos in many-body systems using entanglement as a resource |
| title_full | Diagnosing quantum chaos in many-body systems using entanglement as a resource |
| title_fullStr | Diagnosing quantum chaos in many-body systems using entanglement as a resource |
| title_full_unstemmed | Diagnosing quantum chaos in many-body systems using entanglement as a resource |
| title_short | Diagnosing quantum chaos in many-body systems using entanglement as a resource |
| title_sort | diagnosing quantum chaos in many body systems using entanglement as a resource |
| url | http://doi.org/10.1103/PhysRevResearch.2.013254 |
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