Berezinskii-Kosterlitz-Thouless transitions in the six-state clock model

Abstract

Classical 2D clock model is known to have a critical phase with Berezinskii-Kosterlitz-Thouless(BKT) transitions. These transitions have logarithmic corrections which make numerical analysis difficult. In order to resolve this difficulty, one of the authors has proposed the method called level spectroscopy, which is based on the conformal field theory. We extend this method to the multi-degenerated case. As an example, we study the classical 2D 6-clock model which can be mapped to the quantum self-dual 1D 6-clock model. Additionally, we confirm that the self-dual point has a precise numerical agreement with the analytical result, and we argue the degeneracy of the excitation states at the self-dual point from the effective field theoretical point of view.

18pages, 7figures

References in corpus (3)

• Correlation functions of the 2D sine-Gordon model
• $SU(2)/Z_2$ symmetry of the BKT transition and twisted boundary conditio n
• Level spectroscopy of the square-lattice three-state Potts model with a ferromagnetic next-nearest-neighbor coupling

Cited by in corpus (25)

• Critical properties of the two-dimensional $q$-state clock model
• Topological phases in gapped edges of fractionalized systems
• Response to a twist on systems with Zp symmetry
• Resolving the Berezinskii-Kosterlitz-Thouless transition in the 2D XY model with tensor-network based level spectroscopy
• Phase transitions in the ${\mathbb{Z}}_p$ and U(1) clock models
• Accurate simulation of q-state clock model
• Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Field-induced Berezinskii-Kosterlitz-Thouless transition and string-density plateau in the anisotropic triangular antiferromagnetic Ising model
• Critical behavior of the two-dimensional icosahedron model
• Cross derivative: a universal and efficient method for phase transitions in classical spin models
• Extracting the Luttinger parameter from a single wave function
• Global phase diagram and six-state clock universality behavior in the triangular antiferromagnetic Ising model with anisotropic next-nearest-neighbor coupling: Level-spectroscopy approach
• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
• Dynamical scaling laws in the quantum $q$-state clock chain
• Effective Field Theory of Triangular-Lattice Three-Spin Interaction Model
• Quantum clock models with infinite-range interactions
• Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach
• Phases and Phase Transitions of the Disordered Quantum Clock Model
• Quantum phase diagram for two species hardcore bosons in one-dimensional optical lattices with the resonantly driven Rabi frequency
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• Engineering a Josephson junction chain for the simulation of the clock model
• Deconfined quantum criticality on a triangular Rydberg array
• Compensation in trilayered anisotropic 6-state clock model
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions