Learning phase transitions by confusion

By E. van Nieuwenburg, Ye-Hua Liu, Sebastian D. Huber. Nature Physics, 2016

718 citations recorded by the source corpus.

A neural-network technique can exploit the power of machine learning to mine the exponentially large data sets characterizing the state space of condensed-matter systems. Topological transitions and many-body localization are first on the list. Classifying phases of matter is key to our understanding of many problems in physics. For quantum-mechanical systems in particular, the task can be daunting due to the exponentially large Hilbert space. With modern computing power and access to ever-larger data sets, classification problems are now routinely solved using machine-learning techniques1. Here, we propose a neural-network approach to finding phase transitions, based on the performance of a neural network after it is trained with data that are deliberately labelled incorrectly. We demonstrate the success of this method on the topological phase transition in the Kitaev chain2, the thermal phase transition in the classical Ising model3, and the many-body-localization transition in a disordered quantum spin chain4. Our method does not depend on order parameters, knowledge of the topological content of the phases, or any other specifics of the transition at hand. It therefore paves the way to the development of a generic tool for identifying unexplored phase transitions.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4a9678a38a70429588541518e8ed33995beb4baa

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Machine learning and the physical sciences (2019, methodology): “This idea was explored in (Carrasquilla and Melko, 2017; Morningstar and Melko, 2018; Van Nieuwenburg et al., 2017) in a range of models using configurations sampled uniformly from the model of interest (obtained using Monte Carlo simulations) in different phases and using supervised learning in…”
Quantum Fisher information matrix and multiparameter estimation (2019, methodology): “In recent years, it has been applied to condensed matter physics for phase transitions [193, 194], design of a magneto-optical trap [195] and other aspects [196].”
Discovering physical concepts with neural networks (2018, background): “Mass m = 1kg, amplitude A0 = 1m and phase δ0 = 0 are fixed; spring constant κ ∈ [5, 10] kg/s(2) and damping factor b ∈ [0.”
Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders (2017, methodology): “Phase transitions were found in an unsupervised manner using principle component analysis [24, 25].”
Quantum Entanglement in Neural Network States (2017, background): “It would also be interesting to study entanglement properties in other types of artiﬁcial-neural-network states [33, 34].”