Condensed Matter Theory

Abstract:

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.

Abstract:

We describe a family of phase transitions connecting phases of differing nontrivial topological order by explicitly constructing Hamiltonians of the Levin-Wen type which can be tuned between two solvable points, each of which realizes a different topologically ordered phase. We show that the low-energy degrees of freedom near the phase transition can be mapped onto those of a Potts model, and we discuss the stability of the resulting phase diagram to small perturbations about the model. We further explain how the excitations in the condensed phase are formed from those in the original topological theory, some of which are split into multiple components by condensation, and we discuss the implications of our results for understanding the nature of general achiral topological phases in 2 + 1 dimensions in terms of doubled Chern-Simons theories. © 2011 American Physical Society.