Phase transition of the q-state clock model: duality and tensor renormalization

Abstract

We investigate the critical behavior and the duality property of the ferromagnetic $q$-state clock model on the square lattice based on the tensor-network formalism. From the entanglement spectra of local tensors defined in the original and dual lattices, we obtain the exact self-dual points for the model with $q\le 5$ and approximate self-dual points for $q\ge 6$. We calculate accurately the lower and upper critical temperatures for the six-state clock model from the fixed-point tensors determined using the higher-order tensor renormalization group method and compare with other numerical results.

arXiv comment5 pages, 4 figures

References in corpus (15)

• Efficient classical simulation of slightly entangled quantum computations
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Tensor renormalization group approach to 2D classical lattice models
• Coarse-graining renormalization by higher-order singular value decomposition
• Second Renormalization of Tensor-Network States
• Renormalization of tensor-network states
• Loop optimization for tensor network renormalization
• Dualities and the phase diagram of the $p$-clock model
• Tensor renormalization group study of classical XY model on the square lattice
• Probability-Changing Cluster Algorithm for Two-Dimensional XY and Clock Models
• Universality away from critical points in two-dimensional phase transitions
• Controlling sign problems in spin models using tensor renormalization
• Non-Kosterlitz-Thouless transitions for the $q$-state clock models
• Local scale transformations on the lattice with tensor network renormalization
• DMRG study of the Berezinskii-Kosterlitz-Thouless transitions of the 2D five-state clock model

Cited by in corpus (29)

• Differentiable Programming Tensor Networks
• Machine Learning for Condensed Matter Physics
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Critical properties of the two-dimensional $q$-state clock model
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Tensor network formulation of the massless Schwinger model
• Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO${}_4$ and beyond
• Phase transitions in the ${\mathbb{Z}}_p$ and U(1) clock models
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• 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
• Monte Carlo study of duality and the Berezinskii-Kosterlitz-Thouless phase transitions of the two-dimensional $q$-state clock model in flow representations
• Logarithmic finite-size scaling correction to the leading Fisher zeros in the p-state clock model: A higher-order tensor renormalization group study
• Clock model interpolation and symmetry breaking in O(2) models
• Variational corner transfer matrix renormalization group method for classical statistical models
• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• 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
• A Parallel Computing Method for the Higher Order Tensor Renormalization Group
• Dynamical scaling laws in the quantum $q$-state clock chain
• Phase transitions in $q$-state clock model
• Phases and Phase Transitions of the Disordered Quantum Clock Model
• Self-Supervised Ensemble Learning: A Universal Method for Phase Transition Classification of Many-Body Systems
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase
• Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice
• Tensor renormalization group approach to critical phenomena via symmetry-twisted partition functions
• Variational boundary based tensor network renormalization group
• Two-dimensional $J_1$-$J_2$ clock model: Enhanced symmetries, emergent orders, and Landau-incompatible transitions