Abstract:

Topological phases lack local order parameters that can distiguish them. Their low-energy field theory is not of Ginzburg-Landau type, and, given a many-body ground-state wavefunction of a generic Hamiltonian, it is usually extremely hard to recognize whether the state is topological or not. It was recently proposed by Li and Haldane that the entanglement spectrum can distinguish between states of different topological order. In this talk, I will show how to clearly define an entanglement "order parameter" gap that can distinguish a topological phase. This involves taking the "conformal limit" of a wavefunction, a procedure which removes all intrinsic length-scales of the underlying microscopic problem. I exemplify this on Fractional Quantum Hall states (which are bulk gapped) as well as on gapless spin liquids (where I give a definition of topological order)