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Scaling Theory of Fading Ergodicity
Rafał Świętek1,2, Miroslav Hopjan1,3, Carlo Vanoni4,5
1J. Stefan Institute, Department of Theoretical Physics, SI-1000 Ljubljana, Slovenia.
Physical Review Letters
|November 7, 2025
Summary
A new scaling theory explains ergodicity breaking in interacting quantum systems. It predicts a critical exponent of 1 and suggests one-parameter scaling is insufficient for these complex systems.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Statistical mechanics
Background:
- Noninteracting quantum systems typically follow one-parameter scaling theory for localization.
- A comprehensive theory for many-body ergodicity breaking is currently lacking.
- Ergodicity breaking is a critical phenomenon in quantum systems where they fail to explore all possible states.
Purpose of the Study:
- To introduce a novel scaling theory for ergodicity breaking in interacting quantum systems.
- To address the limitations of one-parameter scaling in complex many-body systems.
- To provide a theoretical framework for understanding ergodicity breaking dynamics.
Main Methods:
- Developed a scaling theory incorporating the Fermi golden rule for divergent relaxation times.
- Applied the fading ergodicity scenario to describe observable fluctuations near the critical point.
- Analyzed the behavior of interacting quantum systems at the ergodicity breaking transition.
Main Results:
- The proposed theory predicts a critical exponent ν=1 at the ergodicity breaking point.
- Demonstrated that one-parameter scaling is generally insufficient for interacting systems.
- Showcased the role of divergent relaxation times and specific fluctuation behaviors.
Conclusions:
- The new scaling theory provides a robust framework for studying ergodicity breaking in interacting systems.
- The findings suggest a need for more sophisticated scaling theories, potentially involving two parameters.
- This work lays the groundwork for future investigations into complex quantum phenomena.
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