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Cornering Gapless Quantum States via Their Torus Entanglement.
William Witczak-Krempa1,2, Lauren E Hayward Sierens3,4, Roger G Melko3,4
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|March 4, 2017
Summary
We analyzed entanglement entropy (EE) in gapless quantum systems. Our findings reveal universal properties and new relations, providing a fingerprint for exotic states like quantum spin liquids.
Area of Science:
- Condensed Matter Physics
- Quantum Information Theory
- Quantum Field Theory
Background:
- Entanglement entropy (EE) is crucial for understanding complex quantum states.
- Gapless systems on tori in 2D and 3D exhibit universal EE properties.
- Scale-invariant systems are key to theoretical analysis.
Purpose of the Study:
- Analyze the universal part of EE (denoted by χ) for gapless systems on tori.
- Derive general nonperturbative properties for the shape dependence of χ.
- Explore relations between χ and EE associated with corners in the entangling surface.
Main Methods:
- Focus on scale-invariant systems.
- Derive general nonperturbative properties for shape dependence.
- Obtain closed-form expressions for χ in 2D and 3D within a CFT model.
- Develop parameter-free Ansätze for 2D and 3D free boson CFTs.
- Perform numerical lattice calculations to validate Ansätze.
Main Results:
- Derived general nonperturbative properties for the shape dependence of χ.
- Revealed surprising relations between χ and corner EE.
- Obtained closed-form expressions for χ in 2D and 3D CFT models.
- Developed highly accurate, parameter-free Ansätze for free boson CFTs.
- Numerical calculations confirmed the high accuracy of the Ansätze.
Conclusions:
- The torus EE serves as a fingerprint for exotic states.
- Demonstrated applicability to gapless quantum spin liquids, such as Kitaev's honeycomb model.
- The derived properties and Ansätze offer a powerful tool for analyzing quantum matter.
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