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Out-of-time-order correlation for many-body localization
Ruihua Fan1, Pengfei Zhang2, Huitao Shen3
1Institute for Advanced Study, Tsinghua University, Beijing 100084, China; Department of Physics, Peking University, Beijing 100871, China.
Out-of-time-order correlators (OTOC) exhibit power-law decay in many-body localized systems, distinguishing them from Anderson localization. A new theorem links OTOC decay to Rényi entropy growth.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- Many-body localization (MBL) is a key phenomenon in disordered quantum systems.
- Understanding the dynamics and distinct phases of localized systems is crucial.
- Out-of-time-order correlators (OTOC) are sensitive probes of quantum chaos and scrambling.
Purpose of the Study:
- To compute OTOC in phenomenological and random-field XXZ models within the MBL phase.
- To investigate the behavior of OTOC at scrambling time in MBL systems.
- To establish OTOC as a tool to differentiate MBL from Anderson localization.
- To derive a general theorem connecting OTOC decay and Rényi entropy growth.
Main Methods:
- Calculation of OTOC for specific quantum models (phenomenological and random-field XXZ).
- Analysis of OTOC behavior in the many-body localized phase.
- Theoretical proof of a theorem relating equilibrium OTOC decay to non-equilibrium dynamics (Rényi entropy).
Main Results:
- OTOC exhibits power-law decay at scrambling time in many-body localized systems.
- OTOC successfully distinguishes many-body localized phase from Anderson localized phase, unlike normal correlators.
- An exact theorem is proven, relating the growth of second Rényi entropy during quench dynamics to the equilibrium decay of OTOC.
Conclusions:
- OTOC provides a robust signature of many-body localization and quantum scrambling.
- The derived theorem offers a fundamental connection between equilibrium and non-equilibrium properties in generic quantum systems.
- These findings advance the understanding of quantum dynamics in localized phases.
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