Quantum Entanglement and Tensor Network RG

For many decades, the Landau theory of symmetry breaking has dominated thinking about phase transitions. Recent interest in topological phases and quantum orders, which lie beyond the realm of symmetry breaking theory. Need a more robust framework. RG provides. I describe how numerical RG can be used to understand phases beyond sym. breaking. Implementation for quantum ordered phases requires introduction of a new approach – entanglement filtered tensor network RG – that I will introduce in this talk. There is hope that using these methods, all strongly correlated systems could be understood, at least numerically. Tall order, but here is the state of play. Outline 1) Overview of topological and quantum orders 2) The RG approach to Phases, and problems. 3) Tensor Network RG 4) Entanglement and entanglement filtering 5) Tensor Network RG applied to spin 1 chain and Haldane Phase 6) Looking ahead.