Title: A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models
Author(s):

	M. Richter-Laskowska (Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland) ,
	H. Khan (Department of Physics, The Ohio State University, 191 W. Woodruff Ave., Columbus, Ohio 43210, USA) ,
	N. Trivedi (Department of Physics, The Ohio State University, 191 W. Woodruff Ave., Columbus, Ohio 43210, USA) ,
	M.M. Maśka (Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland)

The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model.

Key words: phase transitions, topological defects, XY model, artificial neural networks, machine learning
PACS: 64.60.-i, 05.70.Fh, 07.05.Mh

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