Monday, June 29, 1:30pm 6C-442 Speaker: Steve Flammia, U Sydney Title: Fast algorithms for distinguishing topological phases Abstract: Topological phases live at the frontier of our understanding of the low-energy properties of quantum many-body systems. Under plausible physical assumptions, it is believed that such systems are classified abstractly in terms of tensor categories, but it remains to find efficiently computable invariants that uniquely identify the phase given only a candidate Hamiltonian. Here we use the natural connection between topological quantum phases and quantum error-correcting codes to propose a class of invariants that can distinguish abelian topological phases without computing ground states, reduced density operators, topological entropy, excitation spectra, or other "hard to compute" functions of the phase. These invariants are related to Haah's invariants for commuting Hamiltonians, but apply to any gapped Hamiltonian and without any need for computing expectations with respect to ground state wavefunctions. The invariant can be computed by optimizing a one-dimensional cost function using DMRG, which provides a fast heuristic that allows us to distinguish phases that cannot be distinguished using e.g. topological entanglement entropy. Time permitting, I will discuss applications to the theory of quantum error correction and topological quantum computation, as well as possible extensions to the case of nonabelian topological order. This is joint work with Jacob Bridgeman (Sydney) and David Poulin (Sherbrooke). _______________________________________________ qip mailing list qip(a)mit.edu http://mailman.mit.edu/mailman/listinfo/qip