Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks

TL;DR

This paper presents an iterative retraining method using recurrent neural networks to efficiently simulate large quantum many-body systems by leveraging translational invariance and progressively enlarging the model.

Contribution

Introduces a novel iterative retraining approach with RNNs for scalable quantum system simulation, outperforming traditional methods like DMRG in higher dimensions.

Findings

Successfully simulates large 1D and 2D quantum systems

Leverages translational invariance for efficiency

Generalizes better to higher dimensions than DMRG

Abstract

Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce iterative retraining, an approach for simulating bulk quantum systems that uses recurrent neural networks (RNNs). By mapping translations in the lattice vector to the time index of an RNN, we are able to efficiently capture the near translational invariance of large lattices. We show that we can use this symmetry mapping to simulate very large systems in one and two dimensions. We do so by 'growing' our model, iteratively retraining the same model on progressively larger lattices until edge effects become negligible. We argue that this scheme generalizes more naturally to higher dimensions than Density Matrix Renormalization Group.