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

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.

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• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Tensor renormalization group study of (1+1)-dimensional U(1) gauge-Higgs model at $\theta =\pi$ with Lüscher's admissibility condition
• Improved coarse-graining methods on two dimensional tensor networks including fermions
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• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
• Helicity modulus and chiral symmetry breaking for boundary conditions with finite twist
• Phase structure analysis of 2d lattice CP(1) model with $\theta$ term using tensor renormalization group method
• Finite-size scaling on the torus with periodic projected entangled-pair states
• The BKT Transition and its Dynamics in a Spin Fluid
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• Berezinskii-Kosterlitz-Thouless Renormalization Group Flow at a Quantum Phase Transition
• Edge-Edge Correlations without Edge-States: $\eta$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain