Condensed Matter

The simulation of systems of anyons offers a significant challenge to
the condensed matter physicist. These systems are presently of
substantial theoretical and experimental interest due to their potential
for universal quantum computation, but due to their non-trivial exchange
statistics, the tools available for their study have been limited. In
this talk, I will present a formalism whereby any existing tensor
network algorithm may be adapted for use with both Abelian and
non-Abelian anyons, culminating in our recent simulations of infinite

More than forty years ago Nobel laureate P.W. Anderson studied the overlap between two nearby ground states. The result that the overlap tends to zero in the thermodynamics limit was catastrophic for those times. More recently the study of the overlap between ground states, i.e. the fidelity, led to the formulation of the so called fidelity approach to (quantum) phase transition (QPT).

Entanglement renormalization is a coarse-graining transformation for quantum lattice systems. It produces the multi-scale entanglement renormalization ansatz, a tensor network state used to represent ground states of strongly correlated systems in one and two spatial dimensions. In 1D, the MERA is known to reproduce the logarithmic violation of the boundary law for entanglement entropy, S(L)~log L, characteristic of critical ground states. In contrast, in 2D the MERA strictly obeys the entropic boundary law, S(L)~L, characteristic of gapped systems and a class of critical systems.