Department of Physics
Condensed Matter Seminar

Topological phases of matter do not have a local order parameter to characterize them. Given a realistic Hamiltonian, it is very hard to know whether its ground-state is topologically ordered or not, and if so, to which universality class of topological order it corresponds to. In this talk, I will present a new principle of adiabatic continuity based on the Entanglement Spectrum that requires only knowledge of the many-body ground-state of a Hamiltonian and not its full spectrum. I will pick as examples Fractional Quantum Hall states and I will show that if one takes a certain "conformal" limit of the FQH wavefunction then the entanglement spectrum takes a simple form with a series of low energy levels separated by a FULL entanglement gap from a series of spurious, high energy levels. The entanglement adiabatic principle I conjecture then predicts that the topological universality class is preserved as long as the entanglement gap does not close. Numerical work is presented in support of the conjecture.