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Arresting Classical Many-Body Chaos by Kinetic Constraints
Aydin Deger1, Sthitadhi Roy2,3,4, Achilleas Lazarides1
1Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom.
Physical Review Letters
|October 28, 2022
Summary
Kinetic constraints cause a dynamical phase transition in spin chains, leading to a localized phase where chaos freezes. This unexpected localization arises from immobile spin segments called frozen islands.
Area of Science:
- Condensed matter physics
- Quantum chaos
- Statistical mechanics
Background:
- Classical many-body chaos is fundamental to understanding complex systems.
- Out-of-time-ordered correlators (OTOCs) are key diagnostics for quantum chaos.
- Investigating classical analogs of quantum phenomena offers unique insights.
Purpose of the Study:
- To explore the impact of kinetic constraints on classical many-body chaos.
- To identify and characterize dynamical phase transitions in a Heisenberg spin chain.
- To understand the mechanisms behind unexpected localization in chaotic systems.
Main Methods:
- Utilized a classical analog of the out-of-time-ordered correlator (OTOC).
- Studied a translationally invariant Heisenberg spin chain.
- Analyzed the system's behavior under varying strengths of kinetic constraints.
Main Results:
- A "dynamical phase transition" was observed, driven by constraint strength.
- A delocalized phase with ballistic OTOC propagation was identified.
- A localized phase emerged where the OTOC ceased propagation, freezing the system.
- Localization was attributed to the formation of "frozen islands" of immobile spins.
Conclusions:
- Kinetic constraints can induce unexpected localization in classical spin chains.
- The formation of frozen islands is the dominant mechanism for this localization.
- This work provides a classical perspective on chaos and localization phenomena.
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