Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

Abstract

We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor-network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

14 pages, 14 figures

References in corpus (17)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Continuous Matrix Product States for Quantum Fields
• Algorithms for finite Projected Entangled Pair States
• Simulation of fermionic lattice models in two dimensions with Projected Entangled-Pair States: Next-nearest neighbor Hamiltonians
• Monte Carlo simulation with Tensor Network States
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Phase Transitions of Ferromagnetic Potts Models on the Simple Cubic Lattice
• Time evolution of projected entangled pair states in the single layer picture
• Variational Monte Carlo simulations using tensor-product projected states
• High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

Cited by in corpus (33)

• Tensor networks for complex quantum systems
• Hyper-optimized tensor network contraction
• Lecture Notes of Tensor Network Contractions
• Loop optimization for tensor network renormalization
• Anisotropic Tensor Renormalization Group
• Variational tensor network renormalization in imaginary time: benchmark results in the Hubbard model at finite temperature
• Phase transition of four-dimensional Ising model with higher-order tensor renormalization group
• Fast counting with tensor networks
• Accurate simulation for finite projected entangled pair states in two dimensions
• Bond-weighted Tensor Renormalization Group
• Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature
• Automatic Differentiation for Second Renormalization of Tensor Networks
• Tensor Renormalization Group with Randomized Singular Value Decomposition
• Tensor network simulation for the frustrated $J_1$-$J_2$ Ising model on the square lattice
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice
• Few-body systems capture many-body physics: tensor network approach
• Critical analysis of two-dimensional classical XY model
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Phase transitions of the five-state clock model on the square lattice
• Triad second renormalization group
• Efficient calculation of three-dimensional tensor networks
• Infinite Matrix Product States vs Infinite Projected Entangled-Pair States on the Cylinder: a comparative study
• Tensor network method for reversible classical computation
• Dual-isometric Projected Entangled Pair States
• Evaluating the Jones polynomial with tensor networks
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Accuracy and Efficiency of Simplified Tensor Network Codes
• Improved local truncation schemes for the higher-order tensor renormalization group method
• Triad representation for the anisotropic tensor renormalization group in four dimensions
• Efficient 2D Tensor Network Simulation of Quantum Systems
• Variational boundary based tensor network renormalization group
• Electric Field Propagation Through Singular Value Decomposition