Tensor Network Renormalization

Tensor Network Renormalization.

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 upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability...

Plaquette renormalization scheme for tensor network states.

We present a method for contracting a square-lattice tensor network in two dimensions based on auxiliary tensors accomplishing successive truncations (renormalization) of eight-index tensors for 2 × 2 plaquettes into four-index tensors. Since all approximations are done on the wave function (which also can be interpreted in terms of different kinds of tensor networks), the scheme is variational...

Second renormalization of tensor-network states.

We propose a second renormalization group method to handle the tensor-network states or models. This method dramatically reduces the truncation error of the tensor renormalization group. It allows physical quantities of classical tensor-network models or tensor-network ground states of quantum systems to be accurately and efficiently determined.

Neural Network Renormalization Group

We present a variational renormalization group approach using deep generative model composed of bijectors. The model can learn hierarchical transformations between physical variables and renormalized collective variables. It can directly generate statistically independent physical configurations by iterative refinement at various length scales. The generative model has an exact and tractable li...

Tensor Networks: a quantum-information perspective on numerical renormalization groups