Finite temperature ordering of dilute graphene antiferromagnets

We employ large-scale quantum Monte Carlo simulations to study the magnetic ordering transition among dilute magnetic moments randomly localized on the graphene honeycomb lattice, induced by long-ranged RKKY interactions at low charge carrier concentration. In this regime the effective exchange interactions are ferromagnetic within each sublattice, and antiferromagnetic between opposite sublattices, with an overall cubic decay of the interaction strength with the separation between the moments. We verify explicitly, that this commensurability leads to antiferromagnetic order among the magnetic moments below a finite transition temperature in this two-dimensional system. Furthermore, the ordering temperature shows a crossover in its power-law scaling with the moments' dilution from a low- to a high-concentration regime.Comment: 8 pages, 8 figure

Effective models for strong electronic correlations at graphene edges

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.Comment: 13 pages, 9 figure

Z2 topological invariants in two dimensions from quantum Monte Carlo

We employ quantum Monte Carlo techniques to calculate the $Z_2$ topological invariant in a two-dimensional model of interacting electrons that exhibits a quantum spin Hall topological insulator phase. In particular, we consider the parity invariant for inversion-symmetric systems, which can be obtained from the bulk's imaginary-time Green's function after an appropriate continuation to zero frequency. This topological invariant is used here in order to study the trivial-band to topological-insulator transitions in an interacting system with spin-orbit coupling and an explicit bond dimerization. We discuss the accessibility and behavior of this topological invariant within quantum Monte Carlo simulations.Comment: 7 pages, 6 figure

Sleep apnea-hypopnea quantification by cardiovascular data analysis

Sleep apnea is the most common sleep disturbance and it is an important risk factor for cardiovascular disorders. Its detection relies on a polysomnography, a combination of diverse exams. In order to detect changes due to sleep disturbances such as sleep apnea occurrences, without the need of combined recordings, we mainly analyze systolic blood pressure signals (maximal blood pressure value of each beat to beat interval). Nonstationarities in the data are uncovered by a segmentation procedure, which provides local quantities that are correlated to apnea-hypopnea events. Those quantities are the average length and average variance of stationary patches. By comparing them to an apnea score previously obtained by polysomnographic exams, we propose an apnea quantifier based on blood pressure signal. This furnishes an alternative procedure for the detection of apnea based on a single time series, with an accuracy of 82%

Dimerized Solids and Resonating Plaquette Order in SU(N)-Dirac Fermions

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half-filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.Comment: 5 pages, 6 figure

Finite-Temperature Dynamics and Thermal Intraband Magnon Scattering in Haldane Spin-One Chains

The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations and quantum Monte Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal spectral functions, indicative of localized edge-states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to the spin spectral function with an enhanced spectral weight at low momenta and its upper threshold. This emerging thermal spectral feature of the Haldane spin-one chain is shown to result from intra-band magnon scattering due to the thermal population of the single-magnon branch, which features a large bandwidth-to-gap ratio. These findings are discussed with respect to possible future studies on spin-one chain compounds based on inelastic neutron scattering.Comment: 10 pages with 11 figures total (including Supplemental Material); changes in v2: new Figs. S1 and S5, Fig. S3 expanded + related discussion + many smaller modifications to match published versio

Dynamical Signatures of Edge-State Magnetism on Graphene Nanoribbons

We investigate the edge-state magnetism of graphene nanoribbons using projective quantum Monte Carlo simulations and a self-consistent mean-field approximation of the Hubbard model. The static magnetic correlations are found to be short ranged. Nevertheless, the correlation length increases with the width of the ribbon such that already for ribbons of moderate widths we observe a strong trend towards mean-field-type ferromagnetic correlations at a zigzag edge. These correlations are accompanied by a dominant low-energy peak in the local spectral function and we propose that this can be used to detect edge-state magnetism by scanning tunneling microscopy. The dynamic spin structure factor at the edge of a ribbon exhibits an approximately linearly dispersing collective magnonlike mode at low energies that decays into Stoner modes beyond the energy scale where it merges into the particle-hole continuum.Comment: 4+ pages including 4 figure

Quantum Monte Carlo studies of edge magnetism in chiral graphene nanoribbons

We investigate chiral graphene nanoribbons using projective quantum Monte Carlo simulations within the local Hubbard model description and study the effects of electron-electron interactions on the electronic and magnetic properties at the ribbon edges. Static and dynamical properties are analyzed for nanoribbons of varying width and edge chirality, and compared to a self-consistent Hartee-Fock mean-field approximation. Our results show that for chiral ribbons of sufficient width, the spin correlations exhibit exceedingly long correlation lengths, even between zigzag segments that are well separated by periodic armchair regions. Characteristic enhancements in the magnetic correlations for distinct ribbon widths and chiralities are associated with energy gaps in the tight-binding limit of such ribbons. We identify specific signatures in the local density of states and low- energy modes in the local spectral function which directly relate to enhanced electronic correlations along graphene nanoribbons and which can be accessed scanning tunneling spectroscopy.Comment: 11 pages, 15 figure

Antiferromagnetism in the Hubbard Model on the Bernal-stacked Honeycomb Bilayer

Using a combination of quantum Monte Carlo simulations, functional renormalization group calculations and mean-field theory, we study the Hubbard model on the Bernal-stacked honeycomb bilayer at half-filling as a model system for bilayer graphene. The free bands consisting of two Fermi points with quadratic dispersions lead to a finite density of states at the Fermi level, which triggers an antiferromagnetic instability that spontaneously breaks sublattice and spin rotational symmetry once local Coulomb repulsions are introduced. Our results reveal an inhomogeneous participation of the spin moments in the ordered ground state, with enhanced moments at the three-fold coordinated sites. Furthermore, we find the antiferromagnetic ground state to be robust with respect to enhanced interlayer couplings and extended Coulomb interactions.Comment: 4+ pages, 4 figures; final versio

Parallel Mining of Association Rules Using a Lattice Based Approach

The discovery of interesting patterns from database transactions is one of the major problems in knowledge discovery in database. One such interesting pattern is the association rules extracted from these transactions. Parallel algorithms are required for the mining of association rules due to the very large databases used to store the transactions. In this paper we present a parallel algorithm for the mining of association rules. We implemented a parallel algorithm that used a lattice approach for mining association rules. The Dynamic Distributed Rule Mining (DDRM) is a lattice-based algorithm that partitions the lattice into sublattices to be assigned to processors for processing and identification of frequent itemsets. Experimental results show that DDRM utilizes the processors efficiently and performed better than the prefix-based and partition algorithms that use a static approach to assign classes to the processors. The DDRM algorithm scales well and shows good speedup