**abstract:**
Topological order characterizes those phases of matter that defy the standard description in terms of symmetry breaking and local order parameters. Topological order is found in nature in the fractional quantum Hall effect. Topologically ordered systems have ground state degeneracy that is robust against perturbations, which has given the root to topological quantum information processing. We discusss the second order quantum phase transition between a spin-polarized phase and a topologically ordered string-net condensed phase. Next we show how to prepare the topologically ordered phase through adiabatic evolution in a time that is upper bounded by $O(\sqrt{n})$. This provides a physically plausible method for constructing a topological quantum memory. We discuss applications to topological and adiabatic quantum computing.
We present a numerical study of the quantum phase transition from the magnetically ordered phase to the topologically ordered phase of a $n $-spins $1*2$ system. We show that the derivative of von Neumann entropy of a plaquette diverges at the critical point, signaling a second order quantum phase transition. Moreover, we compute the finite-size scaling of the Topological Entropy, showing how this quantity detects the passage to the topologically ordered phase. *

Mon 26 Mar, 17:50 - 18:20, Aula Dini

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