Machine learning quantum phases of matter beyond the fermion sign problem

Area of Science:

• Quantum Many-Body Physics
• Statistical Mechanics
• Machine Learning Applications

Background:

• Machine learning (ML) offers automated methods for distinguishing phases of matter.
• Identifying quantum phase transitions (QPTs) is crucial for understanding complex quantum systems.

Purpose of the Study:

• To optimize convolutional neural networks (CNNs) for identifying QPTs in quantum many-fermion systems.
• To demonstrate the efficacy of ML in analyzing quantum systems, particularly those with a fermion sign problem.

Main Methods:

• Utilized auxiliary-field quantum Monte Carlo (QMC) simulations to sample fermionic systems.
• Employed CNNs to analyze the Green's function obtained from QMC.
• Developed an optimized ML approach for QPT detection.

Main Results:

• CNNs successfully identified and located QPTs in quantum many-fermion systems.
• The Green's function contains sufficient information for phase distinction using CNNs.
• The QMC + ML approach proved effective even for systems with a severe fermion sign problem.

Conclusions:

• CNNs provide a powerful, automated tool for QPT detection in quantum many-fermion systems.
• This ML-driven method overcomes limitations of conventional techniques, especially for systems with fermion sign challenges.
• The study highlights the potential of integrating ML with QMC for advancing statistical mechanics.