DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

Abstract

The two Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional 5-state clock model are studied on infinite strips using the DMRG algorithm. Because of the open boundary conditions, the helicity modulus ${{\rm Y}}_2$ is computed by imposing twisted magnetic fields at the two boundaries. Its scaling behavior is in good agreement with the existence of essential singularities with $\sigma =1/2$ at the two transitions. The predicted universal values of ${{\rm Y}}_2$ are shown to be reached in the thermodynamic limit. The fourth-order helicity modulus is observed to display a dip at the high-temperature BKT transition, like the XY model, and shown to take a new universal value at the low-temperature one. Finally, the scaling behavior of magnetization at the low-temperature transition is compatible with $\eta =1/4$.

arXiv comment12 pages, 13 figures

References in corpus (12)

• The density-matrix renormalization group
• Two-step melting in two dimensions: First-order liquid-hexatic transition
• On the accuracy of the density matrix renormalization group method
• Universality away from critical points in two-dimensional phase transitions
• DMRG studies of critical SU(N) spin chains
• Response to a twist on systems with Zp symmetry
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Numerical study of the phase transitions in the two-dimensional Z(5) vector model
• Direct Evidence of the Discontinuous Character of the Kosterlitz-Thouless Jump
• The XY Model and the Three-state Antiferromagnetic Potts model in Three Dimensions: Critical Properties from Fluctuating Boundary Conditions
• Residual discrete symmetry of the five-state clock model
• The phase transitions in 2D Z(N) vector models for N>4

Cited by in corpus (20)

• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• Critical properties of the two-dimensional $q$-state clock model
• 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
• 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
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Variational corner transfer matrix renormalization group method for classical statistical models
• Partition function zeros of the p-state clock model in the complex temperature plane
• Cross derivative: a universal and efficient method for phase transitions in classical spin models
• Tensor network calculation of the logarithmic correction exponent in the XY model
• Berezinskii-Kosterlitz-Thouless transition from Neural Network Flows
• Numerical study of the critical phases of the frustrated Z(5) model
• Phases and Phase Transitions of the Disordered Quantum Clock Model
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• Helicity modulus in the bilayer XY model by worm algorithm
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions