Variational boundary based tensor network renormalization group
arXiv:2508.10418 · doi:10.1103/w75n-bh3r
Abstract
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment for the entire system. Based on this optimized environment, we construct renormalization projectors that significantly enhance accuracy. By leveraging the canonical form of tensors, our algorithm maintains the same computational complexity as the original tensor renormalization group (TRG) method, yet achieves higher accuracy than existing approaches that do not incorporate entanglement filtering. Our work offers a practical pathway for extending TRG methods to higher dimensions while keeping computational costs manageable.
7 pages, 5 figures
References in corpus (44)
- Efficient classical simulation of slightly entangled quantum computations
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Entanglement renormalization
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- 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
- Tensor networks for complex quantum systems
- Competing states in the t-J model: uniform d-wave state versus stripe state
- Coarse-graining renormalization by higher-order singular value decomposition
- Tensor Network Renormalization
- Algorithms for entanglement renormalization
- Variational optimization algorithms for uniform matrix product states
- Second Renormalization of Tensor-Network States
- Tangent-space methods for uniform matrix product states
- Renormalization of tensor-network states
- Loop optimization for tensor network renormalization
- Faster Methods for Contracting Infinite 2D Tensor Networks
- Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
- Renormalization of tensor networks using graph independent local truncations
- Algorithms for tensor network renormalization
- Gauge fixing, canonical forms and optimal truncations in tensor networks with closed loops
- Critical properties of the two-dimensional -state clock model
- Renormalization group flows of Hamiltonians using tensor networks
- Renormalization group contraction of tensor networks in three dimensions
- Phase transition of the q-state clock model: duality and tensor renormalization
- Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
- Automatic Differentiation for Second Renormalization of Tensor Networks
- Tensor Renormalization Group with Randomized Singular Value Decomposition
- The area law and real-space renormalization
- Entanglement branching operator
- Boundary Tensor Renormalization Group
- Solving frustrated Ising models using tensor networks
- Accurate simulation of q-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
- Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
- Nuclear norm regularized loop optimization for tensor network
- Scaling dimensions from linearized tensor renormalization group transformations
- Global optimization of tensor renormalization group using the corner transfer matrix
- Unified tensor network theory for frustrated classical spin models in two dimensions
- Critical line of the triangular Ising antiferromagnet in a field from a -symmetric corner transfer matrix algorithm
- Matrix product state fixed points of non-Hermitian transfer matrices
- Tensor-Ring Decomposition with Index-Splitting
- Tensor network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice