Exact results for quench dynamics and defect production in a two-dimensional model
K Sengupta1, Diptiman Sen, Shreyoshi Mondal
1TCMP division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064, India.
Physical Review Letters
|March 21, 2008
Summary
We found defect density scales with quench rate in critical systems. The Kitaev model exemplifies this, with new calculations for defect correlations.
Area of Science:
- Condensed Matter Physics
- Quantum Many-Body Systems
Background:
- Understanding critical phenomena and defect formation is crucial in condensed matter physics.
- Quenching systems across critical surfaces leads to defect generation, a key area of study.
Purpose of the Study:
- To develop a theoretical scaling law for defect density during a quench across a critical surface.
- To provide an exact calculation for multispin correlation functions to analyze defect correlations.
- To propose experimental methods for validating the theoretical predictions.
Main Methods:
- Derivation of a scaling law for defect density based on critical exponents (nu and z).
- Application of the scaling law to the two-dimensional Kitaev model (d=2, m=1, nu=1, z=1).
- Exact calculation of multispin correlation functions for defect analysis.
Main Results:
- The defect density (n) scales as approximately 1/tau^(mnu/(znu+1)) with quench rate (tau^-1).
- The Kitaev model precisely fits this scaling law with the specified parameters.
- First exact calculation of multispin correlation functions for defect correlation in a 2D model.
Conclusions:
- The derived scaling law provides a universal description of defect formation across critical surfaces.
- The Kitaev model serves as a concrete example validating the theoretical framework.
- The developed methods and results pave the way for experimental verification and further theoretical exploration.
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