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Anomalous relaxation of density waves in a ring-exchange system
Pranay Patil1,2, Markus Heyl1,3, Fabien Alet2
1Max-Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany.
Physical Review. E
|April 19, 2023
Summary
Stochastic dynamics in a ring-exchange model show long-lasting memory of initial states. Unconventional structure formation explains this slow dynamics, challenging mean-field predictions.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Computational Physics
Background:
- Stochastic dynamics are crucial for understanding complex systems.
- Ring-exchange models exhibit unique behaviors on lattices.
- Previous theories often rely on mean-field approximations.
Purpose of the Study:
- To analyze the slowing down of stochastic dynamics in a ring-exchange model on a square lattice.
- To investigate the preservation of coarse-grained memory in the system.
- To compare simulation results with predictions from continuum theory.
Main Methods:
- Numerical simulations of the ring-exchange model on a square lattice.
- Analysis of correlation functions within dynamically active regions.
- Comparison with low-frequency continuum theory predictions.
Main Results:
- Observed preservation of coarse-grained memory for unexpectedly long times.
- Identified unconventional transient long-range structure formation.
- Demonstrated that slow melting of this structure is key to the slowing-down mechanism.
Conclusions:
- The observed dynamics challenge standard mean-field theory predictions.
- Transient long-range structures play a critical role in the system's slow dynamics.
- Results have implications for quantum ring-exchange models and dipole-conserving systems.
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