Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

Abstract

We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of triangular, kagome, honeycomb, square-octagon, star, ruby, square-hexagon-dodecahedron, and dice lattices. As benchmark tests, we apply the developed method to the classical Ising model on different lattices and observe a remarkable agreement of the results with the available from the literature. The approach also shows the necessary potential to be applied to various quantum lattice models in a combination with the wave-function variational optimization schemes.

29 pages, 47 figures, final version

References in corpus (24)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Tensor renormalization group approach to 2D classical lattice models
• Spin-orbital quantum liquid on the honeycomb lattice
• Tensor Network Algorithms: a Route Map
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Yang-Baxter and the Boost: splitting the difference
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Variational methods for contracting projected entangled-pair states
• Tensor network approach to the two-dimensional fully frustrated XY model and a chiral ordered phase
• Solving frustrated Ising models using tensor networks
• Weak correlation effects in the Ising model on triangular-tiled hyperbolic lattices
• Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Chiral spin liquids on the kagome lattice with projected entangled simplex states
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Unified tensor network theory for frustrated classical spin models in two dimensions
• Variational corner transfer matrix renormalization group method for classical statistical models
• Global optimization of tensor renormalization group using the corner transfer matrix
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Real-space renormalization group approach for the corner Hamiltonian
• Efficient calculation of three-dimensional tensor networks
• Topological dualities via tensor networks

Cited by in corpus (10)

• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Derivation of the free energy, entropy and specific heat for planar Ising models: Application to Archimedean lattices and their duals
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
• Variational optimization of projected entangled-pair states on the triangular lattice
• SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice