Related papers: Machine learning vortices at the Kosterlitz-Thoule…

In this paper, we apply machine learning methods to study phase transitions in certain statistical mechanical models on the two dimensional lattices, whose transitions involve non-local or topological properties, including site and bond…

We propose two machine-learning methods based on neural networks, which we respectively call the phase-classification method and the temperature-identification method, for detecting different types of phase transitions in the XXZ models…

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…

In statistical physics, the XY model in two dimensions provides the paradigmatic example of phase transitions mediated by topological defects (vortices). Over the years, a variety of analytical and numerical methods have been deployed in an…

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…

We demonstrate that a machine learning technique with a simple feedforward neural network can sensitively detect two successive phase transitions associated with the Berezinskii-Kosterlitz-Thouless (BKT) phase in q-state clock models…

We present an analysis of neural network-based machine learning schemes for phases and phase transitions in theoretical condensed matter research, focusing on neural networks with a single hidden layer. Such shallow neural networks were…

We study the XY model on a spherical surface inspired by recently realized spherically confined atomic gases. Instead of a traditional latitude-longitude lattice, we introduce a much more homogeneous spherical lattice, the Fibonacci…

Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in…

Detecting the topological Kosterlitz-Thouless (KT) transition in the prototypical 2D XY model using unsupervised machine learning methods has long been a challenging problem due to the lack of suitable order parameters. To address this…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

Classifying phases of matter is a central problem in physics. For quantum mechanical systems, this task can be daunting owing to the exponentially large Hilbert space. Thanks to the available computing power and access to ever larger data…

The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are…

We consider computer generated configurations of quantised vortices in planar superfluid Bose-Einstein condensates. We show that unsupervised machine learning technology can successfully be used for classifying such vortex configurations to…

The classical XY model has been consistently studied since it was introduced more than six decades ago. Of particular interest has been the two-dimensional spin model's exhibition of the Berezinskii-Kosterlitz-Thouless (BKT) transition.…

A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators…

Using a supervised neural network (NN) trained once on a one-dimensional lattice of 200 sites, we calculate the Berezinskii--Kosterlitz--Thouless phase transitions of the two-dimensional (2D) classical $XY$ and the 2D generalized classical…

The celebrated work of Berezinskii, Kosterlitz and Thouless in the 1970s revealed exotic phases of matter governed by topological properties of low-dimensional materials such as thin films of superfluids and superconductors. Key to this…

Non-trivial topological behavior appears in many different contexts in statistical physics, perhaps the most known one being the Kosterlitz-Thouless phase transition in the two dimensional XY model. We study the behavior of a simpler, one…

In several physical systems, important properties characterizing the system itself are theoretically related with specific degrees of freedom. Although standard Monte Carlo simulations provide an effective tool to accurately reconstruct the…