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Low-temperature hopping dynamics with energy disorder: renormalization group approach
Kirill A Velizhanin1, Andrei Piryatinski, Vladimir Y Chernyak
1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
The Journal of Chemical Physics
|September 7, 2013
Summary
We developed a fast renormalization group (RG) method for analyzing low-temperature hopping in disordered materials. This new RG approach accurately models complex energy landscapes, outperforming traditional methods.
Area of Science:
- Condensed Matter Physics
- Computational Physics
Background:
- Low-temperature hopping dynamics in energy-disordered lattices are crucial for understanding material properties.
- Traditional numerical methods like direct diagonalization can be computationally expensive for these systems.
Purpose of the Study:
- To develop an efficient real-space renormalization group (RG) approach for analyzing low-temperature hopping dynamics.
- To assess the accuracy and computational speed of the proposed RG method compared to existing techniques.
Main Methods:
- Formulation of a real-space renormalization group (RG) approach based on time-scale separation.
- Application of the RG method to one- and two-dimensional lattices with varying energy disorder.
- Analysis of RG flows for energy distribution and Miller-Abrahams pre-exponential factors.
Main Results:
- The proposed RG approach provides accurate results at low temperatures.
- The method is significantly faster than brute-force direct diagonalization.
- Applicability criteria for the RG approach were established based on time-scale separation and hierarchy levels.
Conclusions:
- The developed real-space RG method offers an efficient and accurate alternative for studying hopping dynamics in disordered systems.
- The RG approach simplifies complex dynamics into a hierarchical process, enabling faster computation.
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