A recent theoretical breakthrough has been the identification of new gapped topological phases which only appear in interacting systems, but which, unlike fractional Quantum Hall states or spin liquids, only have short ranged quantum entanglement. Although one dimensional examples – such as the Haldane phase of the spin-1 chain - have been long known, only recently have higher dimensional realizations been proposed based on a mathematical classification scheme, which however leaves open the physical nature of these phases. We will discuss a physical approach in 2D and 3D, that captures the defining properties and an intuitive picture of these states, as well as provides a route to their realization in experimental systems.
 Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach, Yuan-Ming Lu and Ashvin Vishwanath, Phys. Rev. B 86, 125119 (2012)
 Physics of three dimensional bosonic topological insulators: Ashvin Vishwanath and T. Senthil, arXiv:1209.3058