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Published on: May 30, 2014
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Quantum information-geometry of dissipative quantum phase transitions
Leonardo Banchi1, Paolo Giorda1, Paolo Zanardi2
1Institute for Scientific Interchange Foundation, Via Alassio 11/c, 10126 Torino, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 30, 2014
Summary
We developed a new framework to analyze quantum phase transitions in open quantum systems. This fidelity approach uses differential geometry to map phase diagrams and understand critical phenomena.
Area of Science:
- Quantum Physics
- Open Quantum Systems
- Statistical Mechanics
Background:
- Dissipation-driven open quantum systems exhibit novel phase transitions.
- A general analytical framework for these transitions is currently lacking.
- Existing methods do not fully capture the dynamics of open quantum systems.
Purpose of the Study:
- To extend the fidelity approach to analyze quantum phase transitions in open quantum systems.
- To provide a general framework for understanding steady-state phase transitions.
- To explore the differential-geometric and information-theoretic properties of these systems.
Main Methods:
- Extension of the fidelity approach to Gaussian fermionic states.
- Introduction of a metric tensor on the manifold of correlation matrices.
- Analysis of the scaling behavior of the metric tensor.
- Connection to Liouvillean gap and correlation functions.
Main Results:
- The fidelity approach successfully maps the phase diagram of open quantum systems.
- The metric tensor quantifies distinguishability between steady states.
- Scaling behavior of the metric tensor reveals critical phenomena.
- Connections established between fidelity, Liouvillean gap, and correlation functions.
Conclusions:
- The fidelity approach offers a powerful strategy for exploring dissipative quantum critical phenomena.
- Differential geometry and information theory provide key insights.
- This framework enhances the analysis of phase transitions in open quantum systems.
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