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New class of level statistics in correlated disordered chains
Pedro Carpena1, Pedro Bernaola-Galván, Plamen Ch Ivanov
1Departamento de Física Aplicada II. E.T.S.I. de Telecomunicación, Universidad de Málaga, 29071, Málaga, Spain.
Physical Review Letters
|November 5, 2004
Summary
We discovered a critical correlation level in 1D disordered systems. Below this threshold, level statistics are Poissonian; above it, new distributions emerge, altering system behavior.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Disordered systems
Background:
- 1D disordered systems typically exhibit Poisson level statistics.
- Long-range spatial correlations can significantly alter system properties.
- Understanding these correlations is crucial for predicting quantum system behavior.
Purpose of the Study:
- To investigate the impact of long-range spatial correlations on the level statistics of 1D disordered systems.
- To identify critical thresholds in correlation strength that change statistical behavior.
- To characterize the novel distribution functions emerging in correlated systems.
Main Methods:
- Analysis of level statistics in 1D disordered models.
- Systematic variation of the degree of long-range spatial correlations.
- Asymptotic analysis in the limit of large system sizes.
Main Results:
- A threshold in correlation strength was identified.
- Below the threshold, level statistics follow a Poisson distribution.
- Above the threshold, new distribution functions characterize the level statistics, dependent on correlation degree.
- At the threshold, standard deviation converges as a power law with system size.
Conclusions:
- Long-range correlations fundamentally change level statistics in 1D disordered systems beyond a critical point.
- A new universality class for level statistics is identified in the presence of strong correlations.
- The findings necessitate revised theoretical frameworks for disordered systems with spatial correlations.