Machine learning quantum criticality in the spin-1/2 quantum antiferromagnets on the square lattice with plaquette structure

TL;DR

This paper demonstrates how machine learning techniques can classify quantum phases and detect quantum criticality in a spin-1/2 square-lattice model with plaquette structure, offering a new approach in condensed matter physics.

Contribution

It combines reinforcement and supervised machine learning to analyze quantum criticality in a complex spin model, providing results consistent with traditional methods.

Findings

Identified quantum phase transition between paramagnetic and antiferromagnetic states.

Machine learning results agree with coupled cluster and renormalization group methods.

Slight differences in critical coupling values compared to quantum Monte Carlo results.

Abstract

The power of machine learning algorithms to automatically classify different phases of matter and detect quantum phase transitions without necessity to characterize phases by various quantities like local order parameters or topological invariants as in conventional approaches defined machine learning phases of matter as a new research frontier and basic research tool in condensed matter and statistical physics. We study quantum criticality in the spin-1/2 square-lattice J1-J2 model with additional plaquette structure by combination of reinforcement and supervised machine learning techniques. In our calculations the ground-state spin-spin correlation matrices for several system sizes are first found by restricted Boltzmann machine based variational Monte Carlo method, equivalent to reinforcement learning, and then used as a training data for convolutional neural network based supervised machine learning algorithm for phases classification. The model exhibits a quantum phase transition from paramagnetic plaquette resonating valence bond state to an antiferromagnetic state and has been a topic of great interest because of its close connection to cuprate superconductors and possibility of realization in cold atoms experiments. We consider both frustrated and unfrustrated regimes and compare our results with the results obtained previously with other methods. We find that our results are in good agreement with the results obtained by coupled cluster and real space renormalization group methods for both frustrated and unfrustrated regimes. The quantum Monte Carlo and finite-size scaling result for the unfrustrated case however slightly differs from our result for the critical value of the inter-plaquette coupling strength, although the results are still in reasonable agreement.