Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model

Abstract

We investigate the Berezinskii-Kosterlitz-Thouless transitions for the square-lattice six-state clock model with the corner-transfer matrix renormalization group (CTMRG). Scaling analyses for effective correlation length, magnetization, and entanglement entropy with respect to the cutoff dimension $m$ at the fixed point of CTMRG provide transition temperatures consistent with a variety of recent numerical studies. We also reveal that the fixed point spectrum of the corner transfer matrix in the critical intermediate phase of the six-state clock model is characterized by the scaling dimension consistent with the $c=1$ boundary conformal field theory associated with the effective $Z_6$ dual sine-Gordon model.

arXiv comment7 pages, 7 figures, to appear in Phys. Rev. E

References in corpus (25)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Corner Transfer Matrix Renormalization Group Method
• Theory of finite-entanglement scaling at one-dimensional quantum critical points
• Scaling of entanglement support for Matrix Product States
• Entanglement hamiltonians in two-dimensional conformal field theory
• Corner Transfer Matrix Algorithm for Classical Renormalization Group
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Numerical Renormalization Group at Criticality
• Universality away from critical points in two-dimensional phase transitions
• Kosterlitz-Thouless transition of quantum XY model in two dimensions
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Response to a twist on systems with Zp symmetry
• Universal Entanglement Spectra of Gapped One-dimensional Field Theories
• Phase transition of the q-state clock model: duality and tensor renormalization
• Berezinskii-Kosterlitz-Thouless transition on regular and Villain types of $q$-state clock models
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Berezinskii-Kosterlitz-Thouless transitions in the six-state clock model
• Residual discrete symmetry of the five-state clock model
• DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Comment on `Six-state clock model on the square lattice: Fisher zero approach with Wang-Landau sampling'
• Critical behavior of the two-dimensional icosahedron model
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study

Cited by in corpus (18)

• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Finite-size and finite bond dimension effects of tensor network renormalization
• Entropy production at criticality in a nonequilibrium Potts model
• Accurate simulation of q-state clock model
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Clock model interpolation and symmetry breaking in O(2) models
• Commensurate-incommensurate transition in the chiral Ashkin-Teller model
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model
• Comprehensive studies on the universality of BKT transitions -- Machine-learning study, Monte Carlo simulation, and Level-spectroscopy method
• Anisotropic deformation of the 6-state clock model: Tricritical-point classification
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• CTMRG study of the critical behavior of an interacting-dimer model
• Vertex Representation of Hyperbolic Tensor Networks
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group