Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy
Atsushi Ueda, Masaki Oshikawa
Abstract
Berezinskii-Kosterlitz-Thouless transition of the classical XY model is reinvestigated, 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.
Topics & Concepts
Renormalization groupClassical XY modelPhysicsRenormalizationTensor (intrinsic definition)Kosterlitz–Thouless transitionDensity matrix renormalization groupFunctional renormalization groupStatistical physicsSpectroscopySpin (aerodynamics)Condensed matter physicsQuantum mechanicsMathematicsPhase transitionPure mathematicsThermodynamicsQuantum many-body systemsPhysics of Superconductivity and MagnetismQuantum, superfluid, helium dynamics