Ab initio quantum transport through armchair graphene nanoribbons: Streamlines in the current density

We calculate the local current density in pristine armchair graphene nanoribbons (AGNRs) with varying width, $N_\mathrm{C}$, employing a density-functional-theory-based ab initio transport formalism. We observe very pronounced current patterns (streamlines) with threefold periodicity in $N_\mathrm{C}$. They arise as a consequence of quantum confinement in the transverse flow direction. Neighboring streamlines are separated by stripes of almost vanishing flow. As a consequence, the response of the current to functionalizing adsorbates is very sensitive to their placement: adsorbates located within the current filaments lead to strong backscattering, while adsorbates placed in other regions have almost no impact at all.Comment: 7 pages, 11 figure

Ab initio spin-flip conductance of hydrogenated graphene nanoribbons: Spin-orbit interaction and scattering with local impurity spins

We calculate the spin-dependent zero-bias conductance $G_{\sigma\sigma'}$ in armchair graphene nanoribbons with hydrogen adsorbates employing a DFT-based ab initio transport formalism including spin-orbit interaction. We find that the spin-flip conductance $G_{\sigma\bar{\sigma}}$ can reach the same order of magnitude as the spin-conserving one, $G_{\sigma\sigma}$, due to exchange-mediated spin scattering. In contrast, the genuine spin-orbit interaction appears to play a secondary role, only

A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory

In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L>=3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Luescher corrections, TBA and Y-system equations. At L=2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing beta-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken - even in the 't Hooft limit.Comment: 21 pages, LaTeX, BibTeX, pstricks, feynm

The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory

We determine the missing finite-size corrections to the asymptotic one-loop dilatation operator of the real $\beta$-deformed $\mathcal{N}=4$ SYM theory for the gauge groups $U(N)$ and $SU(N)$ in the 't Hooft limit. In the $SU(N)$ case, the absence of the $U(1)$ field components leads to a new kind of finite-size effect, which we call prewrapping. We classify which states are potentially affected by prewrapping at generic loop orders and comment on the necessity to include it into the integrability-based description. As a further result, we identify classes of $n$-point correlation functions which at all loop orders in the planar theory are given by the values of their undeformed counterparts. Finally, we determine the superconformal multiplet structure and one-loop anomalous dimensions of all single-trace states with classical scaling dimension $\Delta_0 \leq 4.5$.Comment: Latex, feynmp, pstricks, 37 pages, 6 tables, v2: formulations improved, references added, typos corrected, v3: typos corrected, matches published versio

Readdressing the trade effect of the Euro: Allowing for currency misalignment

We know that euro-area member countries have absorbed asymmetric shocks in ways that are inconsistent with a common nominal anchor. Based on a reformulation of the gravity model that allows for such bilateral misalignment, we disentangle the conventional trade cost channel and trade effects deriving from 'implicit currency misalignment'. Econometric estimation reveals that the currency misalignment channel exerts a significant trade effect on bilateral exports. We retrieve country specific estimates of the euro effect on trade based on misalignment. This reveals asymmetric trade effects and heterogeneous outlooks across countries for the costs and benefits from adopting the euro. --Euro,gravity model,exchange rates,purchasing power parity,trade imbalances

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb and Gaussian-type operators, that occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both, integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets.Comment: 18 pages, 2 figures; accepted manuscript. v2: supplementary material include

Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors

A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the - ideally short - fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.Comment: 5+1 pages, 2 figures, 3 table