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Measuring Renyi entanglement entropy in quantum Monte Carlo simulations
Matthew B Hastings1, Iván González, Ann B Kallin
1Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, California 93106, USA.
Physical Review Letters
|May 21, 2010
Summary
We developed a quantum Monte Carlo method to measure Renyi entanglement entropy. This new approach efficiently calculates entanglement scaling in quantum systems, confirming the area law for Heisenberg models.
Area of Science:
- Quantum physics
- Condensed matter physics
- Computational physics
Background:
- Entanglement entropy quantifies quantum correlations in many-body systems.
- Calculating entanglement entropy is computationally challenging for large quantum systems.
- The Renyi entanglement entropy is a key measure in quantum information theory.
Purpose of the Study:
- To develop an efficient quantum Monte Carlo (QMC) method for calculating Renyi entanglement entropy.
- To enable the study of entanglement scaling in complex quantum models.
- To verify the area law for entanglement entropy in specific quantum systems.
Main Methods:
- A novel QMC procedure in the valence bond basis.
- Utilizing the expectation value of a unitary Swap operator on two system copies.
- An improved estimator based on the ratio of Swap operators for subregions.
Main Results:
- Demonstrated convergence of Renyi entropy to exact results for a Heisenberg chain.
- Calculated the scaling of Renyi entropy in the 2D Heisenberg model.
- Confirmed the area law for the Néel ground state up to system size L=32.
Conclusions:
- The developed QMC method provides an efficient route to measure Renyi entanglement entropy.
- The method successfully captures entanglement scaling and validates theoretical predictions like the area law.
- This work advances the computational study of quantum entanglement in condensed matter systems.
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