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Information-theoretic differential geometry of quantum phase transitions
Paolo Zanardi1, Paolo Giorda, Marco Cozzini
1Department of Physics and Astronomy, University of Southern California Los Angeles, California 90089-0484, USA.
Physical Review Letters
|October 13, 2007
Summary
Singularities in the Riemannian metric of quantum Hamiltonians signal quantum phase transitions. This framework unifies differential geometry and information theory for studying quantum critical phenomena.
Area of Science:
- Quantum Physics
- Information Theory
- Differential Geometry
Background:
- Quantum Hamiltonians are described by coupling constants.
- Quantum phase transitions mark significant changes in a system's properties.
- Existing methods for studying quantum criticality can be complex.
Purpose of the Study:
- To establish a universal framework for studying quantum phase transitions.
- To connect the geometry of quantum systems with their critical behavior.
- To leverage information theory and differential geometry for quantum critical phenomena.
Main Methods:
- Equipping the manifold of coupling constants with a Riemannian metric.
- Analyzing the singularities of this metric.
- Correlating metric singularities with quantum phase transitions.
Main Results:
- A natural Riemannian metric exists for the coupling constant manifold.
- Singularities of this metric correspond to quantum phase transitions.
- This approach offers a unified geometric and information-theoretic perspective.
Conclusions:
- The Riemannian metric provides a powerful tool for understanding quantum criticality.
- Singularities in this metric serve as indicators of quantum phase transitions.
- This work bridges differential geometry and information theory in the study of quantum systems.
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