Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection

Abstract

We demonstrate how to map out the phase diagram of a two dimensional quantum many body system with no prior physical knowledge by applying deep \textit{anomaly detection} to ground states from infinite projected entangled pair state simulations. As a benchmark, the phase diagram of the 2D frustrated bilayer Heisenberg model is analyzed, which exhibits a second-order and two first-order quantum phase transitions. We show that in order to get a good qualitative picture of the transition lines, it suffices to use data from the cost-efficient simple update optimization. Results are further improved by post-selecting ground-states based on their energy at the cost of contracting the tensor network once. Moreover, we show that the mantra of ``more training data leads to better results'' is not true for the learning task at hand and that, in principle, one training example suffices for this learning task. This puts the necessity of neural network optimizations for these learning tasks in question and we show that, at least for the model and data at hand, a simple geometric analysis suffices.

Submission to SciPost; code and data available at https://github.com/Qottmann/anomaly-detection-PEPS

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Cited by in corpus (11)

• Generalization in quantum machine learning from few training data
• Provably efficient machine learning for quantum many-body problems
• Improved machine learning algorithm for predicting ground state properties
• Variational Quantum Anomaly Detection: Unsupervised mapping of phase diagrams on a physical quantum computer
• Detecting ergodic bubbles at the crossover to many-body localization using neural networks
• Replacing neural networks by optimal analytical predictors for the detection of phase transitions
• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Survey on Computational Applications of Tensor Network Simulations
• Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations