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Quantum phase transitions and bipartite entanglement.
L-A Wu1, M S Sarandy, D A Lidar
1Chemical Physics Theory Group, Department of Chemistry, Center for Quantum Information and Quantum Control, University of Toronto, Ontario M5S 3H6, Canada.
Physical Review Letters
|February 9, 2005
Summary
We reveal a direct link between quantum phase transitions (QPTs) and bipartite entanglement. Our theory shows how energy nonanalyticity in QPTs is mirrored in entanglement measures, offering new insights into quantum systems.
Area of Science:
- Quantum Information Science
- Condensed Matter Physics
Background:
- Quantum phase transitions (QPTs) are fundamental changes in quantum systems at zero temperature.
- Bipartite entanglement quantifies correlations between two subsystems of a quantum state.
Purpose of the Study:
- To establish a general theoretical framework connecting QPTs and bipartite entanglement.
- To identify how different orders of QPTs manifest in entanglement properties.
Main Methods:
- Derivation of a functional relation between reduced density matrices and Hamiltonian eigenvalues.
- Analysis of ground state energy derivatives in relation to entanglement measures.
- Application of the theory to various quantum spin models.
Main Results:
- A direct functional relationship is established between energy nonanalyticity characterizing QPTs and bipartite entanglement.
- First-order QPTs are signaled by density matrix elements.
- Second-order QPTs are indicated by the first derivative of density matrix elements.
Conclusions:
- The study provides a unified understanding of QPTs and entanglement.
- The derived relationships offer a new tool for detecting and characterizing QPTs.
- The findings are broadly applicable to diverse quantum many-body systems.