Machine learning the Renyi entropy of multiple disjoint intervals with neural networks

{getToc} $title={Table of Contents}

Summary

The study calculates the Renyi entropy of multiple disjoint intervals in the one-dimensional transverse-field quantum Ising model (TFQIM) using machine learning methods with neural networks and direct diagonalization of the Hamiltonian. The results from both methods match each other well within errors.

Highlights

• The study uses the improved swapping operation to compute the Renyi entropy with multiple disjoint intervals.
• The machine learning method with neural networks is used to prepare the ground states of the system.
• The direct diagonalization of the Hamiltonian is used to obtain the exact states of the system.
• The Renyi entropy is computed for two, three, and four disjoint intervals in the TFQIM model.
• The results from both methods match each other well within errors.
• The Renyi entropy increases with the magnetic field until it reaches the critical point and then decreases.
• The study demonstrates the applicability of machine learning methods to compute the Renyi entropy with multiple disjoint intervals.

Key Insights

• The study demonstrates the power of machine learning methods in computing the Renyi entropy with multiple disjoint intervals, which is a challenging task using traditional methods.
• The improved swapping operation is a universal approach to computing the Renyi entropy with multiple disjoint intervals, applicable to various quantum systems.
• The Renyi entropy is a valuable tool for understanding the entanglement properties of quantum systems, and this study provides a new avenue for computing it in complex systems.
• The TFQIM model is a paradigmatic model for studying quantum phase transitions, and this study provides new insights into its entanglement properties.
• The study highlights the importance of using multiple methods to verify the accuracy of results, especially when dealing with complex quantum systems.
• The machine learning method with neural networks can be used to study the Renyi entropy in higher-dimensional systems and other complex quantum systems.
• The study opens up new avenues for exploring the entanglement properties of quantum systems using machine learning methods.

Mindmap

If MindMap doesn't load, go to the Homepage and visit blog again or Switch to Android App (Under Development).

Citation

Shi, H.-Q., & Zhang, H.-Q. (2024). Machine learning the Renyi entropy of multiple disjoint intervals with neural networks (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20444