Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy

The discovery of the Berezinskii-Kosterlitz-Thouless transition some fifty years ago was a subject of the 2016 Nobel Prize in Physics. However, quantitative study of the transition in the two-dimensional XY spin model still suffers from significant finite-size effects. The authors implement the level-spectroscopy method, originally developed for quantum systems. They utilize the modern tensor-network renormalization scheme. This allows for an extremely accurate determination of the critical point as well as for a visualization of the celebrated Kosterlitz renormalization-group flow.