Dynamical CPA approach to an itinerant fermionic spin glass model

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.Comment: 9 pages, 6 figures, revised versio

Semi-fermionic representation of SU(N) Hamiltonians

We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is found for arbitrary N. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex distribution functions. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model.Comment: 11 pages, 7 EPS figures included, extended versio

New technique for replica symmetry breaking with application to the SK-model at and near T=0

We describe a novel method which allows the treatment of high orders of replica-symmetry-breaking (RSB) at low temperatures as well as at T=0 directly, without a need for approximations or scaling assumptions. It yields the low temperature order function q(a,T) in the full range $0\leq a <\infty$ and is complete in the sense that all observables can be calculated from it. The behavior of some observables and the finite RSB theory itself is analyzed as one approaches continuous RSB. The validity and applicability of the traditional continuous formulation is then scrutinized and a new continuous RSB formulation is proposed

Selforganized 3-band structure of the doped fermionic Ising spin glass

The fermionic Ising spin glass is analyzed for arbitrary filling and for all temperatures. A selforganized 3-band structure of the model is obtained in the magnetically ordered phase. Deviation from half filling generates a central nonmagnetic band, which becomes sharply separated at T=0 by (pseudo)gaps from upper and lower magnetic bands. Replica symmetry breaking effects are derived for several observables and correlations. They determine the shape of the 3-band DoS, and, for given chemical potential, influence the fermion filling strongly in the low temperature regime.Comment: 13 page

One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin glass model in a transverse field

The one-step replica symmetry breaking (RSB) is used to study a two-sublattice fermionic infinite-range Ising spin glass (SG) model in a transverse field $\Gamma$. The problem is formulated in a Grassmann path integral formalism within the static approximation. In this model, a parallel magnetic field $H$ breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase (SG+AF) characterizing an asymmetric RSB region. In this region, intra-sublattice disordered interactions $V$ increase the difference between the RSB solutions of each sublattice. The freezing temperature shows a higher increase with $H$ when $V$ enhances. A discontinue phase transition from the replica symmetry (RS) solution to the RSB solution can appear with the presence of an intra-sublattice ferromagnetic average coupling. The $\Gamma$ field introduces a quantum spin flip mechanism that suppresses the magnetic orders leading them to quantum critical points. Results suggest that the quantum effects are not able to restore the RS solution. However, in the asymmetric RSB region, $\Gamma$ can produce a stable RS solution at any finite temperature for a particular sublattice while the other sublattice still presents RSB solution for the special case in which only the intra-sublattice spins couple with disordered interactions.Comment: 11 pages, 8 figures, accepted for publication in Phys. Rev.

Dynamical solutions of a quantum Heisenberg spin glass model

We consider quantum-dynamical phenomena in the $\mathrm{SU}(2)$, $S=1/2$ infinite-range quantum Heisenberg spin glass. For a fermionic generalization of the model we formulate generic dynamical self-consistency equations. Using the Popov-Fedotov trick to eliminate contributions of the non-magnetic fermionic states we study in particular the isotropic model variant on the spin space. Two complementary approximation schemes are applied: one restricts the quantum spin dynamics to a manageable number of Matsubara frequencies while the other employs an expansion in terms of the dynamical local spin susceptibility. We accurately determine the critical temperature $T_c$ of the spin glass to paramagnet transition. We find that the dynamical correlations cause an increase of $T_c$ by 2% compared to the result obtained in the spin-static approximation. The specific heat $C(T)$ exhibits a pronounced cusp at $T_c$. Contradictory to other reports we do not observe a maximum in the $C(T)$-curve above $T_c$.Comment: 8 pages, 7 figure

Iteratively reweighted compressive sensing based algorithm for spectrum cartography in cognitive radio networks

© 2014 IEEE. Spectrum cartography is the process of constructing a map showing Radio Frequency signal strength over a finite geographical area. In our previous work we formulated spectrum cartography as a compressive sensing problem and we illustrated how cartography can be used in the context of discovering spectrum holes in space that can be exploited locally in cognitive radio networks. This paper investigates the performance of compressive sensing based approach to cartography in a fading environment where realtime channel estimation is not feasible. To accommodate for lack of channel information we take an iterative approach. We extend the well-known iteratively reweighted ℓ1 minimisation approach by exploiting spatial correlation between two points in space. We evaluate the performance in an urban environment where Rayleigh fading is prominent. Our numerical results show a significant improvement in the probability of accurately making a spectrum sensing decision, in comparison to the well-known weighted approach and the traditional compressive sensing based method

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field $\Gamma$. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean $J_0$ and standard deviation $J$. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small $g$ ($g$ is the strength of the local superconductor coupling written in units of $J$), while the PAIR phase appears as unique solution for large $g$. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of $\Gamma$.Comment: 16 pages, 6 figures, accepted Eur. Phys. J.

Bound hole states in a ferromagnetic (Ga,Mn)As environment

A numerical technique is developed to solve the Luttinger-Kohn equation for impurity states directly in k-space and is applied to calculate bound hole wave functions in a ferromagnetic (Ga,Mn)As host. The rich properties of the band structure of an arbitrarily strained, ferromagnetic zinc-blende semiconductor yields various features which have direct impact on the detailed shape of a valence band hole bound to an active impurity. The role of strain is discussed on the basis of explicit calculations of bound hole states.Comment: 9 pages, 10 figure

Faraday Rotation as a diagnostic of Galactic foreground contamination of CMB maps

The contribution from the residuals of the foreground can have a significant impact on the temperature maps of the Cosmic Microwave Background (CMB). Mostly, the focus has been on the galactic plane, when foreground cleaning has taken place. However, in this paper, we will investigate the possible foreground contamination, from sources outside the galactic plane in the CMB maps. We will analyze the correlation between the Faraday rotation map and the CMB temperature map. The Faraday rotation map is dependent on the galactic magnetic field, as well as the thermal electron density, and both may contribute to the CMB temperature. We find that the standard deviation for the mean cross correlation deviate from that of simulations at the 99.9% level. Additionally, a comparison between the CMB temperature extrema and the extremum points of the Faraday rotation is also performed, showing a general overlap between the two. Also we find that the CMB Cold Spot is located at an area of strong negative cross correlation, meaning that it may be explained by a galactic origin. Further, we investigate nearby supernova remnants in the galaxy, traced by the galactic radio loops. These super nova remnants are located at high and low galactic latitude, and thus well outside the galactic plane. We find some correlation between the Faraday Rotation and the CMB temperature, at select radio loops. This indicate, that the galactic foregrounds may affect the CMB, at high galactic latitudesComment: 13 pages, 22 figures, 6 table