Related papers: Tensor network algorithm by coarse-graining tensor…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based…
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a novel, quantitative understanding of local correlations in a network. Together with a…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
A tensor network renormalization algorithm with global optimization based on the corner transfer matrix is proposed. Since the environment is updated by the corner transfer matrix renormalization group method, the forward-backward iteration…
We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum…
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…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical…
We propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice…
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a…
Regularized factorization is proposed to simulate time evolution for quantum lattice systems. Transcending the Trotter decomposition, the resulting compact structure of the propagator indicates a high-order Baker-Campbell-Hausdorff series.…
We propose a scheme to perform tensor network based finite-size scaling analysis for two-dimensional classical models. In the tensor network representation of the partition function, we use higher-order tensor renormalization group (HOTRG)…
We apply the higher order tensor renormalization group to two and three dimensional relativistic fermion systems on the lattice. In order to perform a coarse-graining of tensor networks including Grassmann variables, we introduce Grassmann…
An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…
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…
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…
We propose a novel algorithm with a modified Tucker decomposition for tensor network that allows for efficiently and precisely calculating the ground state and thermodynamic properties of two-dimensional (2D) quantum spin lattice systems,…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…