The Berezinskii–Kosterlitz–Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models, these are vortices: above a transition temperature TBKT, vortices are free; below this transition temperature, they get confined. In this work, we extend the concept of BKT transition to quantum systems in two dimensions. In particular, we demonstrate that a zero-temperature quantum BKT phase transition driven by a coupling constant can occur in 2D models governed by an effective gauge field theory with a diverging dielectric constant. One particular example is that of a compact U(1) gauge theory with a diverging dielectric constant, where the quantum BKT transition is induced by non-relativistic, purely 2D magnetic monopoles, which can be viewed also as electric vortices. These quantum BKT transitions have the same diverging exponent z as the quantum Griffiths transition but are not related to disorder.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is the prototype of a phase transition driven by the formation and interaction of topological defects in two-dimensional (2D) systems. In typical models these are vortices: above a transition temperature
TBKT vortices are free, below this transition temperature they get confined. In this work we extend the concept of BKT transition to quantum systems in two dimensions. In particular, we demonstrate that a zero-temperature quantum BKT phase transition, driven by a coupling constant can occur in 2D models governed by an effective gauge field theory with a diverging dielectric constant. One particular example is that of a compact U(1) gauge theory with a diverging dielectric constant, where the quantum BKT transition is induced by non-relativistic, purely 2D magnetic monopoles, which can be viewed also as electric vortices. These quantum BKT transitions have the same diverging exponent
z as the quantum Griffiths transition but have nothing to do with disorder.
The Berezinskii-Kosterlitz-Thouless (BKT) transition is a typical topological phase transition defined between binding and unbinding states of vortices and antivortices, which is not accompanied by spontaneous symmetry breaking. It is known that the BKT transition is difficult to detect from thermodynamic quantities such as specific heat and magnetic susceptibility because of the absence of anomaly in free energy and significant finite-size effects. Therefore, methods based on statistical mechanics which are commonly used to discuss phase transitions cannot be easily applied to the BKT transition. In recent years, several attempts to detect the BKT transition using machine-learning methods based on image recognition techniques have been reported. However, it has turned out that the detection is difficult even for machine learning methods because of the absence of trivial order parameters and symmetry breaking. Most of the methods proposed so far require prior knowledge about the models and/or preprocessing of input data for feature engineering, which is problematic in terms of the general applicability. In this article, we introduce recent development of the machine-learning methods to detect the BKT transitions in several spin models. Specifically, we demonstrate the success of two new methods named temperature-identification method and phase-classification method for detecting the BKT transitions in the q-state clock model and the XXZ model. This progress is expected to sublimate the machine-learning-based study of spin models for exploring new physics beyond simple benchmark test.