Complex Networks from Classical to Quantum

Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information physics is setting the stage for a theory of complex systems with quantum information-inspired methods. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have been proposed to offer enhancement for several network problems. Here we review the results at the cutting edge, pinpointing the similarities and the differences found at the intersection of these two fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio

Bipartite entanglement entropy in fractional quantum Hall states

We present a detailed analysis of bipartite entanglement entropies in fractional quantum Hall (FQH) states, considering both abelian (Laughlin) and non-abelian (Moore-Read) states. We derive upper bounds for the entanglement between two subsets of the particles making up the state. We also consider the entanglement between spatial regions supporting a FQH state. Using the latter, we show how the so-called topological entanglement entropy of a FQH state can be extracted from wavefunctions for a limited number of particles.Comment: 12 pages, 7 figures, small corrections to table III and references adde

Conformal field theory out of equilibrium: a review

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects. These concern the understanding of quantum transport and its statistics at and near critical points. Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain. We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states. Using this we review the theory for energy transport in homogeneous one-dimensional critical systems, including the complete description of its large deviations and the resulting (extended) fluctuation relations. We generalize some of these ideas to one-dimensional critical charge transport and to the presence of defects, as well as beyond one-dimensional criticality. We describe non-equilibrium transport in free-particle models, where connections are made with generalized Gibbs ensembles, and in higher-dimensional and non-integrable quantum field theories, where the use of the powerful hydrodynamic ideas for non-equilibrium steady states is explained. We finish with a list of open questions. The review does not assume any advanced prior knowledge of conformal field theory, large-deviation theory or hydrodynamics.Comment: 50 pages + 10 pages of references, 5 figures. v2: minor modifications. Review article for special issue of JSTAT on nonequilibrium dynamics in integrable quantum system

Community Structure of the Physical Review Citation Network

We investigate the community structure of physics subfields in the citation network of all Physical Review publications between 1893 and August 2007. We focus on well-cited publications (those receiving more than 100 citations), and apply modularity maximization to uncover major communities that correspond to clearly-identifiable subfields of physics. While most of the links between communities connect those with obvious intellectual overlap, there sometimes exist unexpected connections between disparate fields due to the development of a widely-applicable theoretical technique or by cross fertilization between theory and experiment. We also examine communities decade by decade and also uncover a small number of significant links between communities that are widely separated in time.Comment: 14 pages, 7 figures, 8 tables. Version 2: various small additions in response to referee comment