Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy

TL;DR

This paper advances the understanding of the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model by combining tensor network renormalization with level spectroscopy, achieving highly accurate critical point determination and visualizing the RG flow.

Contribution

It introduces a novel approach combining TNR and level spectroscopy to precisely analyze the BKT transition in the 2D XY model, surpassing previous accuracy.

Findings

Accurate critical point determination with reduced logarithmic corrections.

Visualization of the Kosterlitz RG flow based on numerical data.

Order of magnitude improvement over previous methods.

Abstract

Berezinskii-Kosterlitz-Thouless transition of the classical XY model is re-investigated, combining the Tensor Network Renormalization (TNR) and the Level Spectroscopy method based on the finite-size scaling of the Conformal Field Theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gives a visualization of the celebrated Kosterlitz Renormalization Group flow based on the numerical data.