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

TL;DR

This paper introduces a method to map phase diagrams of 2D quantum systems using deep anomaly detection on tensor network ground states, reducing the need for extensive training data and neural network optimization.

Contribution

It presents a novel approach combining anomaly detection with tensor network simulations to identify phase transitions without prior physical knowledge.

Findings

Simple update optimization suffices for qualitative phase diagram mapping.

Post-selection based on energy improves results with minimal additional cost.

One training example can be enough for effective anomaly detection in this context.

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.