Tensor network method

The tensor network method is the method for studying many-body problems based on the tensor network representation (a partially or fully contracted product of many tensors). It is used for computing partition functions of models in classical statistical mechanics as well as ground-state properties of quantum systems in discrete space. In particular, variational principle calculation based with the tensor network state (TNS) is well-known. A TNS is a wave function of which the expansion coefficients in some orthonormal basis are expressed as a product of tensors. Typically, the number of tensors is proportional to the system’s degrees of freedom. When the tensors are of rank 3, the TNS is a matrix product state, and the resulting tensor network method corresponds to DMRG. Similar to DMRG, an arbitrary quantum state can be expressed as a TNS. There are multiple choices for the structure of the network, the method of optimizing the tensors, and the method of contracting network. The tensor network method is a general name referring to all of those.