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Entanglement entropy at infinite-randomness fixed points in higher dimensions
Yu-Cheng Lin1, Ferenc Iglói, Heiko Rieger
1Theoretische Physik, Universität des Saarlandes, 66041, Saarbrücken, Germany.
Physical Review Letters
|October 13, 2007
Summary
The entanglement entropy in a 2D random transverse Ising model shows a unique divergence at its quantum phase transition. A double-logarithmic correction to the area law was discovered, differing from higher-dimensional models.
Area of Science:
- Condensed matter physics
- Quantum magnetism
- Statistical mechanics
Background:
- The transverse Ising model is a fundamental model in condensed matter physics.
- Understanding entanglement entropy is crucial for characterizing quantum phases of matter.
- Strong disorder can lead to novel quantum critical phenomena.
Purpose of the Study:
- To investigate the entanglement entropy of the two-dimensional random transverse Ising model.
- To identify the asymptotic behavior of entanglement entropy near quantum phase transitions.
- To characterize the nature of the infinite-randomness fixed point in this system.
Main Methods:
- Numerical implementation of the strong-disorder renormalization group (SDRG).
- Analysis of the entanglement entropy per surface area.
- Identification of multiplicative corrections to the area law.
Main Results:
- The entanglement entropy per surface area diverges at the quantum phase transition.
- This divergence is governed by an infinite-randomness fixed point.
- A double-logarithmic multiplicative correction to the area law for entanglement entropy was identified.
Conclusions:
- The two-dimensional random transverse Ising model exhibits a distinct behavior at its quantum phase transition compared to higher dimensions.
- The identified double-logarithmic correction provides new insights into entanglement scaling in disordered quantum systems.
- The study highlights the importance of dimensionality in the context of entanglement entropy in disordered models.
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