No abstract

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed ChernSimons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the chargevortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called

We study the entanglement of an impurity at one end of a spin chain with a block of spins using negativity as a true measure of entanglement to characterize the unique features of the gapless Kondo regime in the spin-chain Kondo model. For this spin chain in the Kondo regime we determine-with a true entanglement measure-the spatial extent of the Kondo screening cloud, we propose an ansatz for its ground state and demonstrate that the impurity spin is indeed maximally entangled with the cloud. To better evidence the peculiarities of the Kondo regime, we carry a parallel analysis of the entanglement properties of the Kondo spin-chain model in the gapped dimerized regime. Our study shows how a genuine entanglement measure stemming from quantum information theory can fully characterize also nonperturbative regimes accessible to certain condensed matter systems.

The thermodynamic properties of non interacting bosons on a complex network can be strongly affected by topological inhomogeneities. The latter give rise to anomalies in the density of states that can induce Bose-Einstein condensation in low dimensional systems also in absence of external confining potentials. The anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit. We present a rigorous result providing the general conditions for the occurrence of Bose-Einstein condensation on complex networks in presence of anomalous spectral regions in the density of states. We present results on spectral properties for a wide class of graphs where the theorem applies. We study in detail an explicit geometrical realization, the comb lattice, which embodies all the relevant features of this effect and which can be experimentally implemented as an array of Josephson Junctions.