Generative Deep Learning for the Two-Dimensional Quantum Rotor Model

TL;DR

This paper develops GAN-based generative models to efficiently analyze ground states and phase transitions in the two-dimensional quantum rotor model, demonstrating reduced computational costs and accurate critical point detection.

Contribution

Introduces novel GAN architectures with adaptive loss functions for quantum many-body problems, improving sample generation and phase transition analysis.

Findings

Efficient generation of valid ground-state samples

Accurate identification of critical points in QRM

Reduced computational time for simulations

Abstract

The advancement of diverse generative deep learning models and their variants has furnished substantial insights for investigating quantum many-body problems. In this work, we design two models based on the foundational architecture of generative adversarial networks (GANs) to investigate the ground-state properties and phase transition characteristics of the two-dimensional quantum rotor model (QRM). Within a semi-supervised learning framework, we incorporate multiple layers of transposed convolutions in the generator, enabling the conditional GAN to more efficiently extract low-dimensional encoded information. Analysis of one-dimensional latent variables associated with ground-state samples for different system sizes allows us to pinpoint the location of the critical point. In addition, we introduce dynamically adaptive weighting factors related to the distributional characteristics into the loss function of the deep convolutional GAN, and utilize upsampling techniques to enlarge the generated sample sizes. Comparisons of the optimization processes for mean magnetization and potential energy density across different magnetization regimes of QRM demonstrate that our model can efficiently generate valid ground-state samples, significantly reducing computational time. Our results highlight the promising potential of generative deep learning in quantum phase transition research, especially in critical point identification and the auxiliary generation of simulation data for quantum many-body models.