Abstract
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.
Highlights
In many cases, thermodynamic phase transitions are clearly visible with well defined and identifiable critical points
We have demonstrated how the accuracy of finding the BKT transition in three different models depends on the range of temperatures at which the artificial neural networks (ANN) was trained
One can see there that the section of P(T) that indicates the BKT transition is much steeper than the temperature dependence of the magnetization, even if the network was trained on the extreme temperatures [figure 5 (a)]
Summary
Thermodynamic phase transitions are clearly visible with well defined and identifiable critical points. One example are topological phase transitions, connected to the formation of topological defects, such as dislocations in two-dimensional crystals, vortices in two-dimensional superconductors and so on. The proliferation of these defects leads to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition [1,2,3,4] where thermodynamic quantities behave smoothly. The standard approach is based on the scaling properties of, e.g., the spin stiffness or superfluid density. This is difficult for quantum models, where numerical methods are usually very involved and memory- and time-consuming
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