Phase diagrams of one-, two-, and three-dimensional quantum spin systems

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network representation of the ground state wave-function. Three spin-1/2 models (Ising, XY, XXZ, all in a transverse field) are investigated. Infinite imaginary-time evolution (iTEBD in 1D, ‘simple update’ in 2D and 3D) is used to determine the ground states of these models. The phase structure of the models is discussed for all three dimensions.