In recent years, an increasing number of systems displaying exotic quantum states like unconventional superconductivity, quantum spin-liquids, or topological states were experimentally found. Here we summarize findings in quantum Monte Carlo simulations of correlated electrons on a honeycomb lattice, the structure of graphene, that revealed an unexpected spin-liquid emerging between a state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. Moreover, we found that this quantum-disordered state is a resonating valence-bond (RVB) liquid, akin to the one proposed for high temperature superconductors. This was the first unbiased determination of a RVB-liquid in an electronic system.

A new mechanism is proposed for the magnetization reversal of molecular nanomagnets such as Fe₈. In this process the spin tunnels from the lowest state near one easy direction to the first excited state near the opposite easy direction, and subsequently decays to the second easy direction with the emission of a phonon, or it first emits a phonon and then tunnels to the final state. This mechanism is the simplest imaginable one that allows magnetization relaxation in the presence of a longitudinal magnetic field that is so large that the nuclear spin environment cannot absorb the energy required for energy conservation to hold. It is proposed as a way of understanding both magnetization realaxation and Landau-Zener-Stückelberg (LZS) experiments. The requisite Fermi golden rule rate, and the spin-flip rates are calculated. The rates are too low to affect the minima in the LZS tunneling as a function of transverse field, and also somewhat low for relaxation. Thus a full understanding of magnetic relaxation in the experiments remains an open question.

The Heisenberg exchange parameters for the Heusler compound Co₂NiGa with L2₁ structure were calculated using the Korringa–Kohn–Rostoker method and by employing the magnetic-force theorem to obtain the total energy changes associated with the local rotation of magnetization direction. The crystal structure was subjected to pressure and the corresponding dependence of the magnetic exchange couplings were determined. Curie temperatures obtained by applying mean field theory (MFT) reveals a slightly nonlinear decrease with pressure and it is related to the changes of the magnetic moment and the electronic density of states. Further investigation of the pressure dependence of the Curie temperature and magnetization suggests that this particular compound is a weak itinerant ferromagnet. Analysis of the magnetic properties of the Co₂NiGa compound using Monte Carlo simulations reveals a significant effect of pressure on the magnetization and magnetic susceptibility of the structure. The spin dynamics was modeled by applying the Landau-Lifshitz-Ginzburg equation to a Heisenberg Hamiltonian. The magnon spectra along the [100] direction is obtained through the Fourier transform of the dynamic correlation function for the predefined set of exchange parameters and pressure. We find a large dependence of the magnon dispersion relation with pressure and in particular of the magnetic excitations gap.

In this brief communication, the charge susceptibility, χ_c,imp, is calculated for the single impurity Anderson model in the Kondo regime with the density matrix renormalization group theory (DMRG). Excellent agreement with the Bethe-Ansatz (BA) results is found in the appropriate limit where the (effective) level broadening Γ^☆ and the charging energy, U, are much smaller than the conduction electron bandwidth, D. Deviations occur for large interactions U>D, where we find that χ_c,imp decays faster, approximately by a factor D/U, as compared to the BA-prediction. Our work is of methodological relevance, e.g., for studies of the Kondo-effect in molecular systems, in the sense that it prepares treatments of (spinful) few-orbital models in the Kondo regime.

Using the theory of diffusion in graphs, we propose a model to study mesoscopic transport through a diffusive quantum dot. The graph consists of three quasi-1D regions: a central region describing the dot, and two identical left- and right- wires connected to leads, which mimic contacts of a real system. We find the exact solution of the diffusion equation for this graph and evaluate the conductance including quantum corrections. Our model is complementary to the RMT-models describing quantum dots. Firstly, it reproduces the universal limit at zero temperature. But the main advantage compared to RMT-models is that it allows one to take into account interaction-induced dephasing at finite temperatures. Besides, the crossovers from open to almost closed quantum dots and between different regimes of dephasing can be described within a single framework. We present results for the temperature dependence of the weak localization correction to the conductance for the experimentally relevant parameter range and discuss the possibility to observe the elusive 0D-regime of dephasing in different mesoscopic systems.

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential µ and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

A model system for the injection of fermionic particles from filled source sites into an empty chain is investigated. The ensuing dynamics for Hermitian as well as for non-Hermitian time evolution, where the particles cannot return to the bath sites (quantum ratchet), is studied. A non-homogeneous hybridization between bath and chain sites permits transient currents in the chain. Non-interacting particles show decoherence in the thermodynamic limit: the average particle number and the average current density in the chain become stationary for long times, whereas the single-particle density matrix displays large fluctuations around its mean value. Using the numerical time-dependent density-matrix renormalization group (t-DMRG) method it is demonstrated, on the other hand, that sizable density-density interactions between the particles introduce relaxation which is by orders of magnitudes faster than the decoherence processes.

A three-level system with partially broken SU(3) symmetry immersed in a metal, comprised of a unique non-interacting ground state and two-fold degenerate excited states, exhibits a stable two-channel Kondo fixed point within a wide range of parameters, as has been shown in previous work. Such systems can, for instance, be realized by protons dissolved in a metal and bound in the interstitial space of the host lattice, where the degeneracy of excited rotational states is guaranteed by the space inversion symmetry of the lattice. We analyze the robustness of the 2CK fixed point with respect to a level splitting of the excited states and discuss how this may explain the behavior of the well-known dI/dV spectra measured by Ralph and Buhrman on ultrasmall quantum point contacts in a magnetic field.

In recent years germanium has been emerging as a mainstream material that could have important applications in the microelectronics industry. The principle aim of this study is to review investigations of the diffusion of technologically important p- and n-type dopants as well as surface and interface passivation issues in germanium. The diffusion of impurities in germanium is interrelated to the formation of clusters whenever possible, and possibilities for point defect engineering are discussed in view of recent results. The importance of electrically active defects on the Ge surface and interfaces is addressed considering strategies to suppress them and to passivate the surfaces/interfaces, bearing in mind their importance for advanced devices.

Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar–tensor representation. Modified gravity has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration with no need of a dark energy component or an inflation field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to general relativity, the well-known Brans–Dicke theory. As a novelty, here both theories are studied using a conformal transformation and writing the actions in the Einstein frame, where spherically symmetric solutions are studied using perturbation techniques. The differences between both theories are analyzed as well as the validity of the theorem within the Jordan and Einstein frames, where interesting results are obtained.

Radial slave boson representations have the particular advantage that the expectation values of their respective fields are finite even without the formal introduction of spurious Bose condensates for each of the bosonic fields. The expectation values of the radial (real) fields are in fact to be interpreted as the density of empty or singly occupied sites. Whereas the radial representation of the Barnes slave bosons has been investigated before, a setup for the functional integral of radial bosonic fields in the more physical Kotliar-Ruckenstein representation has not been accomplished to date. We implement a path integral procedure with suitable renormalization factors for a strongly correlated two-site model which allows to control the formal steps in the intricate evaluation, as the results for the partition function and the expectation values are known from exact diagonalization for such a minimal single impurity Anderson model. The partition function is shown to be a trace over a product of matrices local in time and therefore can be calculated analytically. Eventually, we establish the scheme for the evaluation of correlation functions and thermodynamic properties.

The linear electromagnetic response of a uniform three-dimensional electron gas to a longitudinal electric field is determined by the known Lindhard dielectric function ϵ_qω. Using a similar approach, we derive exact analytical expressions for the second-order nonlinear electromagnetic response of the electron gas. We calculate the second-order polarizability α⁽²⁾_qω of the system and, within the self-consistent-field approach, the second-order response function, analogous to ϵ_qω. The best conditions for the observation of the second-harmonic generation are analyzed.

The paper is devoted to an explanation of the accelerated rate of expansion of the Universe. Usually the acceleration of the Universe, which is described by FRW metric, is due to dark energy. It is shown that this effect may be considered as a manifestation of torsion tensor for a flat Universe in the realm of Teleparallel gravity. An observer with radial field velocity obey Hubble's Law. As a consequence it is established that this is radial acceleration in a flat Universe. In Eq. (35) the acceleration is written in terms of the deceleration parameter, the Hubble’s constant and the proper distance. This may be interpreted as an acceleration of the Universe.

In Josephson junction arrays, vortices form stable topological excitations. A key step towards the understanding of their properties was the observation made by Eckern and Schmid that in low-capacitance junction arrays a vortex behaves as a massive particle moving in a periodic potential and subject to dissipation. The mass is low and quantum effects become observable. The present contribution provides a review of these properties together with a discussion of similar scenarios realized in optical lattices.

Spin-orbit interaction is usefully classified as extrinsic or intrinsic, depending on its origin: the potential due to random impurities (extrinsic), or the crystalline potential associated with the band or device structure (intrinsic). In this paper we will show how, by using a SU(2) formulation, the two sources may be described in an elegant and unified way. As a result we obtain a simple description of the interplay of the two types of spin-orbit interaction, and a physically transparent explanation of the vanishing of the d.c. spin Hall conductivity in a Rashba two-dimensional electron gas when spin relaxation is neglected, as well as its reinstatement when spin relaxation is allowed. Furthermore, we obtain an explicit formula for the transverse spin polarization created by an electric current, which generalizes the standard formula obtained by Edelstein, and Aronov and Lyanda-Geller by including extrinsic spin-orbit interaction and spin relaxation.

Methods of charge projectors using special gauge transformations for tagging particles are presented. Such engineering of a many-body wave function allows extracting information regarding properties of a physical system beyond average values. The method is first used to establish under which circumstances the properties of particle currents can be understood as discrete transfers of particles from one region to another. Next, the method is extended to show that in a tunnel junction coupled to a two-level system, the transmission of electrical noise causes decoherence and thereby a projective measurement of the two-level system as encoded by the amount of tunnelled charge. Finally the method is extended to deal with the exceptional circumstance where a measurement on a system with a large number of particles gives macroscopically distinguishable outcomes that are unpredictable, the observed interference pattern of interfering BEC's.

The center graph shows the tunable double-control quantum interference as the detuning frequencies vary. As the two-photon resonance occurs (i.e., δ_p- δ_c = 0 or δ_p- δ_c' = 0), the “double-control interference” parameter Δ drastically changes. Picture: J. Qi Shen, p. 85 in this issue. Background graph taken from C. Emary, C. Pöltl, T. Brandes, Phys. Rev. B 80, 235321 (2009) http://prb.aps.org/abstract/PRB/v80/i23/e235321, © 2009 by The American Physical Society).

There are solutions of Maxwell equations in vacuum in which the magnetic and the electric lines have a nontrivial topology. This behaviour has physical consequences since it is related to classical expressions indicating aspects of the photon content of the electromagnetic field. In this work we present for the first time an exact solution of Maxwell equations in vacuum, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field. We calculate the temporal evolution of the magnetic and electric helicities, and explain the exchange of helicity making use of the Chern-Simon form. We also have found and explained that, as time goes to infinity, both helicities reach the same value and the exchange between the magnetic and electric part of the field stops.

There are solutions of Maxwell equations in vacuum in which the magnetic and the electric lines have a nontrivial topology. This behavior has physical consequences since it is related to classical expressions indicating aspects of the photon content of the electromagnetic field. In this work an exact solution of Maxwell equations in vacuum is presented, having non trivial topology, in which there is an exchange of helicity between the electric and magnetic part of such field.

We study f(R)-gravity with torsion in presence of the most general ELKO matter, checking the consistency of the conservation laws with the matter field equations; we discuss some mathematical features of the field equations in connection with a cosmological application.

A study of f(R)-gravity with torsion in the presence of the most general ELKO matter is presented, checking the consistency of the conservation laws with the matter field equations. In addition, some mathematical features of the field equations in connection with a cosmological application are discussed.

Multilevel quantum coherence and its quantum-vacuum counterpart, where a three-level dark state is involved, are suggested in order to achieve new photonic and quantum optical applications. It is shown that such a three-level dark state in a four-level tripod-configuration atomic system consists of three lower levels, where constructive and destructive quantum interference between two control transitions (driven by two control fields) arises. We point out that the controllable optical response due to the double-control tunable quantum interference can be utilized to design some fascinating new photonic devices such as logic gates, photonic transistors and switches at quantum level. A single-photon two-input XOR logic gate (in which the incident “gate” photons are the individual light quanta of the two control fields) based on such an effect of optical switching control with an EIT (electromagnetically induced transparency) microcavity is suggested as an illustrative example of the application of the dark-state manipulation via the double-control quantum interference. The present work would open up possibility of new applications in both fundamental physics (e.g., field quantization and relevant quantum optical effects in artificial systems that can mimic atomic energy levels) and applied physics (e.g., photonic devices such as integrated optical circuits at quantum level).

Multilevel quantum coherence and its quantum-vacuum counterpart are suggested in order to achieve new photonic and quantum optical applications. It is shown that a three-level dark state in a four-level tripod-configuration atomic system consists of three lower levels, where quantum interference between two control transitions arises. It is pointed out that the controllable optical response can be utilized to design some fascinating new photonic devices such as logic gates, photonic transistors and switches at quantum level.

We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin-0⁺ and spin-0^- modes. To this end we are considering a very appropriate situation – homogeneous-isotropic cosmologies – which is relatively simple, and yet all the modes have non-trivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies. Here the first order equations obtained from an effective Lagrangian are linearized and the normal modes are found. These turn out to control the asymptotic late time cosmological normal modes. Numerical evolution confirms the late time asymptotic approximation and shows the expected effects of the cross parity pseudoscalar coupling.

The dynamics of a new Poincaré gauge theory of gravity model is investigated, which has cross coupling between the spin-0+ and spin-0-modes. To this end a homogeneous-isotropic cosmologies is considered which is relatively simple, and yet all the modes have non-trivial dynamics which reveals physically interesting and possibly observable results. More specifically, an isotropic Bianchi class A cosmologies has been investigated.

We show that in the trapped ion-laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb-Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.

It is shown that in the trapped ion-laser interaction all the regimes may be considered analytically. This applies not only for different laser intensities, but also away from resonance and from the Lamb-Dicke regime. A dispersive Hamiltonian for the high intensity regime is found, that, being diagonal, allows for an easy calculation of the evolution operator.