Concatenated tensor network states

Full text: We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can very efficiently describe time evolution and can possess arbitrary block-wise entanglement and long-ranged correlations. We illustrate the approach for the enhancement of matrix product states, i.e. 1D tensor networks, where we replace each of the matrices of the original matrix product state with another 1D tensor network. This procedure yields a 2D tensor network, which includes - already for tensor dimension two - all states that can be prepared by circuits of polynomially many (possibly non-unitary) two-qubit quantum operations, as well as states resulting from time evolution with respect to Hamiltonians with shortranged interactions. We investigate the possibility to efficiently extract information from these states, which serves as the basic step in a variational optimization procedure. To this aim we utilize known and improved methods for 2D networks. We generalize the approach to higher dimensional and tree tensor networks. (author)