Making the world from topological order

From Lisbon to the World...

Explanation of Theoretical Basics of Analysis of the World Order

From Majorana fermions to topological order.

We consider a system consisting of a 2D network of links between Majorana fermions on superconducting islands. We show that the fermionic Hamiltonian modeling this system is topologically ordered in a region of parameter space: we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Isi...

Topological order from quantum loops and nets

I define models of quantum loops and nets that have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With the appropriate inner product, these quantum loop models are equivalent to net models whose topological weight involves the chromatic polynomial. A simple Hamiltonian preserving the topological order is found ...

Fibonacci topological order from quantum nets.

We analyze a model of quantum nets and show it has a non-Abelian topological order of doubled-Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins aroun...