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Scaling behavior for a class of quantum phase transitions
Wen-ge Wang1, Pinquan Qin, Qian Wang
1Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China. wgwang@ustc.edu.cn
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
Quantum phase transitions with a single bosonic zero mode exhibit universal scaling. Metric quantities like fidelity and Loschmidt echo depend only on the critical parameter ratio, simplifying analysis.
Area of Science:
- Quantum physics
- Condensed matter theory
- Quantum information
Background:
- Quantum phase transitions (QPTs) are fundamental phenomena.
- Models like the Dicke and Lipkin-Meshkov-Glick models exhibit QPTs with a single bosonic zero mode.
- Understanding critical behavior is crucial for quantum technologies.
Purpose of the Study:
- To investigate the scaling properties of metric quantities near quantum phase transitions.
- To demonstrate a universal relationship for fidelity and Loschmidt echo.
- To simplify the analysis of critical phenomena in specific quantum models.
Main Methods:
- Analysis of metric quantities (fidelity, Loschmidt echo) in quantum systems.
- Focus on quantum phase transitions with a single bosonic zero mode.
- Derivation of scaling relations based on the critical parameter ratio.
Main Results:
- Metric quantities, including fidelity, depend solely on the ratio of distances to the critical point.
- This universal scaling holds for both static (fidelity) and time-dependent (Loschmidt echo) quantities.
- Time-dependent quantities scale when time is measured in units of the critical mode's inverse frequency.
Conclusions:
- A universal scaling law governs metric quantities at quantum phase transitions with a single bosonic zero mode.
- This finding simplifies the characterization of critical behavior in models like the Dicke and Lipkin-Meshkov-Glick models.
- The results have implications for quantum information processing and understanding quantum criticality.
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