Uniform random generation of large acyclic digraphs

Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of the structure itself is of great interest. As well as for the assessment of different structure learning algorithms in simulation studies, a uniform sample from the space of directed acyclic graphs is required to evaluate the prevalence of certain structural features. Here we analyse how to sample acyclic digraphs uniformly at random through recursive enumeration, an approach previously thought too computationally involved. Based on complexity considerations, we discuss in particular how the enumeration directly provides an exact method, which avoids the convergence issues of the alternative Markov chain methods and is actually computationally much faster. The limiting behaviour of the distribution of acyclic digraphs then allows us to sample arbitrarily large graphs. Building on the ideas of recursive enumeration based sampling we also introduce a novel hybrid Markov chain with much faster convergence than current alternatives while still being easy to adapt to various restrictions. Finally we discuss how to include such restrictions in the combinatorial enumeration and the new hybrid Markov chain method for efficient uniform sampling of the corresponding graphs.Comment: 15 pages, 2 figures. To appear in Statistics and Computin

Anomalous spin Hall effects in Dresselhaus (110) quantum wells

Anomalous spin Hall effects that belong to the intrinsic type in Dresselhaus (110) quantum wells are discussed. For the out-of-plane spin component, antisymmetric current-induced spin polarization induces opposite spin Hall accumulation, even though there is no spin-orbit force due to Dresselhaus (110) coupling. A surprising feature of this spin Hall induction is that the spin accumulation sign does not change upon bias reversal. Contribution to the spin Hall accumulation from the spin Hall induction and the spin deviation due to intrinsic spin-orbit force as well as extrinsic spin scattering, can be straightforwardly distinguished simply by reversing the bias. For the inplane component, inclusion of a weak Rashba coupling leads to a new type of $S_y$ intrinsic spin Hall effect solely due to spin-orbit-force-driven spin separation.Comment: 6 pages, 5 figure

Universality of the Kondo effect in quantum dots with ferromagnetic leads

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. In most odd Coulomb valleys the Kondo resonance exhibits a pronounced splitting, which depends on the tunnel coupling to the leads and an external magnetic field $B$, and only weakly on gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on $g \mu_B (B-B_c) / k_B T_K$, where $T_K$ is the Kondo temperature and $B_c$ the external field compensating the splitting.Comment: 4 pages, 4 figure

Dielectric function of the semiconductor hole liquid: Full frequency and wave vector dependence

We study the dielectric function of the homogeneous semiconductor hole liquid of p-doped bulk III-V zinc-blende semiconductors within random phase approximation. The single-particle physics of the hole system is modeled by Luttinger's four-band Hamiltonian in its spherical approximation. Regarding the Coulomb-interacting hole liquid, the full dependence of the zero-temperature dielectric function on wave vector and frequency is explored. The imaginary part of the dielectric function is analytically obtained in terms of complicated but fully elementary expressions, while in the result for the real part nonelementary one-dimensional integrations remain to be performed. The correctness of these two independent calculations is checked via Kramers-Kronig relations. The mass difference between heavy and light holes, along with variations in the background dielectric constant, leads to dramatic alternations in the plasmon excitation pattern, and generically, two plasmon branches can be identified. These findings are the result of the evaluation of the full dielectric function and are not accessible via a high-frequency expansion. In the static limit a beating of Friedel oscillations between the Fermi wave numbers of heavy and light holes occurs.Comment: 16 pages, 11 figures included. Update: Minor additions and adjustments, published versio

Ancilla-assisted sequential approximation of nonlocal unitary operations

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the "no-go" theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary entanglers. Despite the negative response from the "no-go" theorem, we demonstrate explicitly how the matrix-product operator(MPO) formalism provides a flexible structure to develop protocols for sequential implementation of such entanglers with an optimal fidelity. The proposed numerical technique, that we call variational matrix-product operator (VMPO), offers a computationally efficient tool for characterizing the "globalness" and entangling capabilities of nonlocal unitary operations.Comment: Slightly improved version as published in Phys. Rev.

Statistical description of eigenfunctions in chaotic and weakly disordered systems beyond universality

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on a generalization of Berry's Random Wave Model, combined with a consistent semiclassical representation of spatial two-point correlations. We derive closed expressions for arbitrary wavefunction averages in terms of universal coefficients and sums over classical paths, which contain, besides the supersymmetry results, novel oscillatory contributions. Their physical relevance is demonstrated in the context of Coulomb blockade physics

Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review Letters; final version (v2) for publication with minor editorial change

Polarization-sensitive absorption of THz radiation by interacting electrons in chirally stacked multilayer graphene

We show that opacity of a clean multilayer graphene flake depends on the helicity of the circular polarized electromagnetic radiation. The effect can be understood in terms of the pseudospin selection rules for the interband optical transitions in the presence of exchange electron-electron interactions which alter the pseudospin texture in momentum space. The interactions described within a semi-analytical Hartree--Fock approach lead to the formation of the topologically different broken--symmetry states characterized by Chern numbers and zero-field anomalous Hall conductivities.Comment: 6 pages, final versio

Parallelization of the exact diagonalization of the t-t'-Hubbard model

We present a new parallel algorithm for the exact diagonalization of the $t-t'$-Hubbard model with the Lanczos-method. By invoking a new scheme of labeling the states we were able to obtain a speedup of up to four on 16 nodes of an IBM SP2 for the calculation of the ground state energy and an almost linear speedup for the calculation of the correlation functions. Using this algorithm we performed an extensive study of the influence of the next-nearest hopping parameter $t'$ in the $t-t'$-Hubbard model on ground state energy and the superconducting correlation functions for both attractive and repulsive interaction.Comment: 18 Pages, 1 table, 8 figures, Latex uses revtex, submitted to Comp. Phys. Com

Vortices in Quantum Spin Systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices.Comment: Remarks added and conclusions enlarged, version to be published in European Physical Journal