Neural network approach for correlated quantum materials
Abstract
Correlated quantum systems are important in condensed matter physics because interactions between particles can lead to rich collective phenomena, while also making these systems difficult to solve numerically. A major challenge is the exponential growth of the Hilbert space with system size, which strongly limits conventional numerical methods such as exact diagonalization. In this work, a neural network approach is studied as an alternative method for approximating the ground-state properties of correlated quantum spin systems. The transverse-field Ising model and the AKLT model are chosen as benchmark systems. First, a multilayer perceptron neural network with full-wavefunction input is constructed and tested on the transverse-field Ising model. The trained energy is found to converge close to the exact diagonalization result for small system sizes. The network is then improved by using a single spin configuration as input and one wavefunction amplitude as output, giving a more compact and more physical representation of the many-body state. To further improve the performance, variational Monte Carlo is combined with the neural network for the transverse-field Ising model, replacing full Hilbert-space summation by stochastic sampling and extending the accessible system size up to 30 spins. The neural network is also adapted to AKLT model, and the trained energy for the 10-spin chain converges very close to the exact result. The results show that neural networks can…
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