In these techniques, the coefficients of the wave function of the quantum many-body states are written as a network of individual tensors based on the amount and structure of entanglement present in them.
In this talk, I will summarize some of the works I have been doing in this direction by using these modern techniques in 1D and 2D systems. In particular, I will use Matrix Product States (MPS) to investigate a spin-2 quantum chain and show the emergence of different effective spin-1 ‘Haldane-like’ Symmetry Protected Topological (SPT) phases and their phase transitions. I will then show how I use the iPEPS (infinite Projected Entangled Pair States) algorithm to study frustrated systems such as the kagome lattice for the XXZ model. I will also discuss a new algorithm which we proposed recently based on iPEPS to study dissipative open quantum systems in 2D. In addition, I will mention some possible future work based on these results.