Learning phase transitions by confusion

Abstract

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 techniques 1 . 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 chain 2 , the thermal phase transition in the classical Ising model 3 , and the many-body-localization transition in a disordered quantum spin chain 4 . 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.Machine learning as a tool for analysing data is becoming more and more prevalent in an increasing number of fields. This is due to a combination of availability of large amounts of data and the advances in hardware and computational power, the latter most notably through the use of graphical processing units.Two typical methods of machine learning can be distinguished, namely the unsupervised and supervised methods. In the former the machine receives no input other than the data and is asked, for example, to extract features or to cluster the samples. Such an unsupervised approach was applied to identify phase transitions and order parameters from images of classical configurations of Ising models 5 . In the supervised learning methods, the data have to be supplemented by a set of labels. A typical example is classification of data, where each sample is assigned a class label. The machine is trained to recognize samples and predict their associated label, demonstrating that it has learned by generalizing to samples it has not encountered before. This approach, too, has been demonstrated on Ising models Motivated by previous studies, we apply machine-learning techniques to the detection of phase transitions. In contrast to the earlier works, however, we focus on a combination of supervised and unsupervised techniques. In most cases, namely, it is exactly the labelling that one would like to find out (that is, classification of phases). That implies that a labelling is not known beforehand, and hence supervised techniques are not directly applicable. In this Letter we demonstrate that it is possible to find the correct labels, by purposefully mislabelling the data and evaluating the performance of the machine learner. We will base our method on NNs, which are capable of fitting arbitrary nonlinear functions 11 . Indeed, if a linear feature extraction method worked, there would have been no need to explicitly find labels in the first place.We emphasize the main result in this work is...

Probing many-body localization with neural networks

“…In physics, the application of neural networks, and machine learning in general, to many-body quantum mechanics is a novel and burgeoning field of research [1]. Currently, there are three main lines of pursuit: the application of machine learning to the problem of classifying various phases of matter [2][3][4][5][6][7][8][9], accelerating material searches and design [10][11][12][13], and the quest to encode quantum mechanical states in structures mimicking the setup of a neural network [14][15][16]. This work is concerned with the first kind of approach.…”

“…Here, we instead use entanglement spectra [17], which in recent years emerged as a powerful tool to characterize a plethora of physical systems, and have been employed for a neural network based detection of phase transitions in Ref. [8].…”

Learning phase transitions from dynamics

“…So far, these methods have relied only on static properties of the underlying physical systems, such as raw state configurations sampled from Monte Carlo simulations [1,15] or entanglement spectra obtained using exact diagonalization [3,11,17]. However, dynamics of physical observables are often more accessible experimentally.…”

“…Machine learning is emerging as a novel tool for identifying phases of matter [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. At its core, this problem can be cast as a classification problem in which data obtained from physical systems are assigned a class (i.e., a phase) using machine learning methods.…”

“…At its core, this problem can be cast as a classification problem in which data obtained from physical systems are assigned a class (i.e., a phase) using machine learning methods. This approach has enabled the autonomous detection of order parameters [2,5,6], phase transitions [1,3], and entire phase diagrams [4,7,16,17]. Simultaneous research effort at the interface between machine learning and many-body physics has focused on the use of neural networks for efficient representations of quantum wave functions [18][19][20][21][22][23][24][25][26], drawing a parallel between deep networks and the renormalization group [27][28][29].…”