Sampling motif-constrained ensembles of networks

The statistical significance of network properties is conditioned on null models which satisfy spec- ified properties but that are otherwise random. Exponential random graph models are a principled theoretical framework to generate such constrained ensembles, but which often fail in practice, either due to model inconsistency, or due to the impossibility to sample networks from them. These problems affect the important case of networks with prescribed clustering coefficient or number of small connected subgraphs (motifs). In this paper we use the Wang-Landau method to obtain a multicanonical sampling that overcomes both these problems. We sample, in polynomial time, net- works with arbitrary degree sequences from ensembles with imposed motifs counts. Applying this method to social networks, we investigate the relation between transitivity and homophily, and we quantify the correlation between different types of motifs, finding that single motifs can explain up to 60% of the variation of motif profiles.Comment: Updated version, as published in the journal. 7 pages, 5 figures, one Supplemental Materia

Pseudogap and antiferromagnetic correlations in the Hubbard model

Using the dynamical cluster approximation and quantum monte carlo we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping $t'$. In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long range antiferromagnetic correlations. The physics in the proximity of $(0,\pi)$ is dramatically influenced by $t'$ and determined by the short range correlations. The effect of $t'$ on the low energy ARPES spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility, produce a concomitant gap in the single-particle spectra near $(\pi,\pi/2)$ but not necessarily at a location in the proximity of Fermi surface.Comment: 5 pages, 4 figure

Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions

We study the magnetic structure of the ground state of an itinerant Fermi system of spin-\nicefrac{1}{2} particles with magnetic dipole-dipole interactions. We show that, quite generally, the spin state of particles depend on its momentum, i.e., spin and orbital degrees of freedom are entangled and taken separately are not ``good'' quantum numbers. Specifically, we consider a uniform system with non-zero magnetization at zero temperature. Assuming the magnetization is along $z$-axis, the quantum spin states are $\v{k}$-dependent linear combinations of eigenstates of the $\sigma_z$ Pauli matrix. This leads to novel spin structures in \textit{momentum space} and to the fact that the Fermi surfaces for ``up'' and ``down'' spins are not well defined. The system still has a cylindrical axis of symmetry along the magnetization axis. We also show that the self energy has a universal structure which we determine based on the symmetries of the dipolar interaction and we explicitly calculated it in the Hartree-Fock approximation. We show that the bare magnetic moment of particles is renormalized due to particle-particle interactions and we give order of magnitude estimates of this renormalization effect. We estimate that the above mentioned dipolar effects are small but we discuss possible scenarios where this physics may be realized in future experiments.Comment: 10 pages, 6 figures(2 subfigures); 4 appendices. Version published in Physical Review

Warped Fermions and Precision Tests

We analyze the behavior of Standard Model matter propagating in a slice of AdS_5 in the presence of infrared-brane kinetic terms. Brane kinetic terms are naturally generated through radiative corrections and can also be present at tree level. The effect of the brane kinetic terms is to expell the heavy KK modes from the infrared-brane, and hence to reduce their coupling to the localized Higgs field. In a previous work we showed that sizable gauge kinetic terms can allow KK mode masses as low as a few TeV, compatible with present precision measurements. We study here the effect of fermion brane kinetic terms and show that they ameliorate the behavior of the theory for third generation fermions localized away from the infrared brane, reduce the contribution of the third generation quarks to the oblique correction parameters and mantain a good fit to the precision electroweak data for values of the KK masses of the order of the weak scale.Comment: 25 pages, 4 figures, latex2

Topological phases and topological entropy of two-dimensional systems with finite correlation length

We elucidate the topological features of the entanglement entropy of a region in two dimensional quantum systems in a topological phase with a finite correlation length $\xi$. Firstly, we suggest that simpler reduced quantities, related to the von Neumann entropy, could be defined to compute the topological entropy. We use our methods to compute the entanglement entropy for the ground state wave function of a quantum eight-vertex model in its topological phase, and show that a finite correlation length adds corrections of the same order as the topological entropy which come from sharp features of the boundary of the region under study. We also calculate the topological entropy for the ground state of the quantum dimer model on a triangular lattice by using a mapping to a loop model. The topological entropy of the state is determined by loop configurations with a non-trivial winding number around the region under study. Finally, we consider extensions of the Kitaev wave function, which incorporate the effects of electric and magnetic charge fluctuations, and use it to investigate the stability of the topological phase by calculating the topological entropy.Comment: 17 pages, 4 figures, published versio

Crystallization Mechanism of Hard Sphere Glasses

In supercooled liquids, vitrification generally suppresses crystallization. Yet some glasses can still crystallize despite the arrest of diffusive motion. This ill-understood process may limit the stability of glasses, but its microscopic mechanism is not yet known. Here we present extensive computer simulations addressing the crystallization of monodisperse hard-sphere glasses at constant volume (as in a colloid experiment). Multiple crystalline patches appear without particles having to diffuse more than one diameter. As these patches grow, the mobility in neighbouring areas is enhanced, creating dynamic heterogeneity with positive feedback. The future crystallization pattern cannot be predicted from the coordinates alone: crystallization proceeds by a sequence of stochastic micro-nucleation events, correlated in space by emergent dynamic heterogeneity.Comment: 4 pages 4 figures Accepted for publication in Phys. Rev. Lett., April 201