Learning a compass spin model with neural network quantum states

Area of Science:

• Quantum physics
• Condensed matter physics
• Computational physics

Background:

• Neural network quantum states offer a new way to represent many-body quantum systems.
• Frustrated quantum spin models are challenging for traditional numerical methods.

Purpose of the Study:

• To investigate the capability of neural network quantum states in describing complex magnetic orders.
• To assess the performance of restricted Boltzmann machines (RBMs) in rugged energy landscapes.

Main Methods:

• Application of restricted Boltzmann machines (RBMs) and stochastic gradient descent.
• Seeking ground states of a compass spin model on a honeycomb lattice.
• Analysis of variational energy, order parameters, and correlation functions.

Main Results:

• The phase diagram of the compass spin model was accurately determined.
• Results align well with tensor network ansatz predictions for frustrated quantum spin Hamiltonians.
• Demonstrated RBMs' capacity in learning ground states of challenging quantum systems.

Conclusions:

• Restricted Boltzmann machines are effective for solving frustrated quantum spin models.
• Neural network quantum states show promise for complex magnetic order investigations.
• Identified limitations and proposed strategies for future machine learning applications in quantum magnetism.