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 (14)
- 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
- Phase transition of the q-state clock model: duality and tensor renormalization
- The area law and real-space renormalization
- Entanglement branching operator
- Accurate simulation of q-state clock model
- 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 network renormalization approach to antiferromagnetic 6-state clock model on the Union Jack lattice