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.

arXiv comment29 pages, 47 figures, final version

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• 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