Quantum magnetism describes systems of magnetic spins in which quantum mechanical effect dominate. It hosts a lot of exotic quantum entangled phases of matter such as the quantum spin liquid that may serve a promising platform for quantum computing. We try to understand the properties and nature of exciting magnetic systems arising from strong correlations and many-body effects.

Theoretical and computatoinal studies on the stronly correlated systems are entering a new phase under the remarkable development in the tensor network algorithm. Advantage of the tensor network representation is not only technical but also conceptual; information on the entanglement is directly accessible by looking at the geomentry of the tensor network and gauge symmetry of local tensors. We study exotic phases of matter such as the Abelian and non-Abelian topological states in the language of the tensor network. We also try to develop a new algorithm to handle the tensor network from the perspective of information science.