Korbinian Kottmann, Philippe Corboz, Maciej Lewenstein, Antonio Acín
SciPost Phys. 11, 025 (2021) ·
published 9 August 2021
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· pdf
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.
Mr Kottmann: "Concerning the first paragraph..."
in Submissions | report on Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection