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Entanglement entropy flow and the Ward identity
Vladimir Rosenhaus1, Michael Smolkin2
1Center for Theoretical Physics and Department of Physics, University of California, Berkeley, California 94720, USA and Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|January 24, 2015
Summary
We developed equations for entanglement entropy flow, linking Weyl transformations to coupling changes. This confirms the trace Ward identity and expresses entropy for free fields using the energy-momentum tensor.
Area of Science:
- Theoretical Physics
- Quantum Information Theory
- String Theory
Background:
- Entanglement entropy quantifies quantum correlations in quantum field theories.
- Understanding its behavior under transformations is crucial for theoretical physics.
Purpose of the Study:
- To derive differential equations for entanglement entropy flow.
- To establish a connection between metric transformations and coupling variations.
- To apply the formalism to massive free fields.
Main Methods:
- Derivation of differential equations for entanglement entropy.
- Analysis of local Weyl transformations and coupling changes.
- Utilizing the trace Ward identity.
Main Results:
- Established a relationship between variations in entanglement entropy under Weyl transformations and coupling changes.
- Demonstrated this relationship is equivalent to the trace Ward identity.
- Expressed entanglement entropy for massive free fields as a two-point function of the energy-momentum tensor.
Conclusions:
- The derived formalism provides a new way to study entanglement entropy.
- The connection to the trace Ward identity offers deeper insights into quantum field theories.
- The application to free fields validates the utility of the formalism.
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