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Entanglement and criticality in quantum impurity systems
Karyn Le Hur1, Philippe Doucet-Beaupré, Walter Hofstetter
1Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
Physical Review Letters
|October 13, 2007
Summary
Entanglement between a spin and its environment is enhanced at quantum phase transitions in impurity systems. This study reveals a maximum in entanglement entropy at criticality, with implications for nanosystems.
Area of Science:
- Quantum physics
- Condensed matter physics
- Mesoscopic systems
Background:
- Impurity systems can exhibit quantum phase transitions between delocalized and localized spin states.
- Entanglement quantifies correlations between quantum systems, such as a spin and its environment.
Purpose of the Study:
- To investigate the behavior of entanglement entropy in impurity systems undergoing a quantum phase transition.
- To explore the relationship between quantum criticality and environmental entanglement.
Main Methods:
- Utilized the spin-boson model with a sub-Ohmic bosonic bath (spectral density J(omega) ~ omega^s, 0 < s < 1).
- Employed Wilson's numerical renormalization group (NRG) method.
- Applied hyperscaling relations to analyze entanglement properties.
Main Results:
- Demonstrated that entanglement entropy is consistently enhanced at the quantum phase transition.
- Observed a distinct cusp (maximum) in the entanglement entropy at the critical point.
- Established a direct correspondence between quantum criticality and impurity entanglement entropy.
Conclusions:
- Quantum phase transitions in impurity systems lead to enhanced spin-environment entanglement.
- The findings are relevant for understanding and designing nanoscale quantum devices.
- Entanglement entropy serves as a sensitive indicator of quantum critical phenomena.
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