Machine learning detection of Berezinskii-Kosterlitz-Thouless transitions in 
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-state clock models

Miyajima, Yusuke; Murata, Yusuke; Tanaka, Yasuhiro; Mochizuki, Masahito

doi:10.1103/physrevb.104.075114

Cited by 26 publications

(14 citation statements)

References 35 publications

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“…2(c) should not be interpreted as the BKT transition points. This on the one hand clarifies that quantitatively identifying critical points via LFRU is restricted to continuous phase transitions, and on the other hand provides data-driven evidence that the transitions in these systems are not of the Landau type, corroborating recent investigations [61][62][63].…”

supporting

confidence: 83%

“…2(c). Noticing that the phase transitions associated with the intermediate phase in these two models are of the BKT type, i.e., driven by topological defects [61][62][63], the po-sitions of the two maxima of heat capacity C(T ) in fact do not exactly match the critical temperatures [61], indicating that the positions of the two minima of regression uncertainty U (T ) in Fig. 2(b) and Fig.…”

mentioning

confidence: 98%

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Learning Phase Transitions from Regression Uncertainty

Guo¹,

Li²

2022

Preprint

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For performing regression tasks involved in various physics problems, enhancing the precision, or equivalently reducing the uncertainty of the regression results is undoubtedly one of the central goals. Here, somewhat surprisingly, we find that the unfavorable regression uncertainty in performing regression tasks of inverse statistical problems actually contains "hidden" information concerning phase transitions of the system under consideration. By utilizing this "hidden" information, we develop a new unsupervised machine learning approach dubbed "learning from regression uncertainty" for automated detection of phases of matter, with the core working horse being a neural network performing regression tasks instead of classification tasks as in various related machine learning approaches developed so far. This is achieved by revealing an intrinsic connection between regression uncertainty and response properties of the system under consideration, thus making the results of this machine learning approach directly interpretable. We demonstrate the approach by identifying the critical point of the ferromagnetic Ising model and revealing the existence of the intermediate phase in the six-state and seven-state clock models. Our approach paves the way towards intriguing possibilities for unveiling new physics via machine learning in an interpretable manner.

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supporting

confidence: 83%

mentioning

confidence: 98%

Learning Phase Transitions from Regression Uncertainty

Guo¹,

Li²

2022

Preprint

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“…For these reasons, the determination of the critical parameters has always been a challenging task if compared with other kinds of phase transitions. Recently, some explicit attempts to address this task by means of machine learning algorithms were made [10,11,[16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

et al. 2022

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The detection of phase transitions in quantum many-body systems with lowest possible prior knowledge of their details is among the most rousing goals of the flourishing application of machine-learning techniques to physical questions. Here, we train a Generative Adversarial Network (GAN) with the Entanglement Spectrum of a system bipartition, as extracted by means of Matrix Product States ansätze. We are able to identify gapless-to-gapped phase transitions in different one-dimensional models by looking at the machine inability to reconstruct outsider data with respect to the training set. We foresee that GAN-based methods will become instrumental in anomaly detection schemes applied to the determination of phase-diagrams.

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“…The labels are usually our target, namely to which phases the data belong. Supervised methods can indeed learn phases efficiently when the labels are available, [9][10][11][12][13][14][15][16][17][18][19][20][21] but their applications are limited since in most cases the labels are unavailable. In contrast, unsupervised methods do not require labels.…”

Section: Introductionmentioning

confidence: 99%

A simple framework for contrastive learning phases of matter

Xiao-Qi¹,

Xu²,

Zhu³

et al. 2022

Preprint

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A main task in condensed-matter physics is to recognize, classify, and characterize phases of matter and the corresponding phase transitions, for which machine learning provides a new class of research tools due to the remarkable development in computing power and algorithms. Despite much exploration in this new field, usually different methods and techniques are needed for different scenarios. Here, we present SimCLP: a simple framework for contrastive learning phases of matter, which is inspired by the recent development in contrastive learning of visual representations. We demonstrate the success of this framework on several representative systems, including classical and quantum, single-particle and many-body, conventional and topological. SimCLP is flexible and free of usual burdens such as manual feature engineering and prior knowledge. The only prerequisite is to prepare enough state configurations. Furthermore, it can generate representation vectors and labels and hence help tackle other problems. SimCLP therefore paves an alternative way to the development of a generic tool for identifying unexplored phase transitions.

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Machine learning detection of Berezinskii-Kosterlitz-Thouless transitions in q -state clock models

Cited by 26 publications

References 35 publications

Learning Phase Transitions from Regression Uncertainty

Learning Phase Transitions from Regression Uncertainty

Detection of Berezinskii-Kosterlitz-Thouless transition via Generative Adversarial Networks

A simple framework for contrastive learning phases of matter

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