Density-operator theory of orbital magnetic susceptibility in periodic insulators

The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.Comment: 5 pages including 2 figures; accepted for publication in Phys. Rev.

Topological Computation without Braiding

We show that universal quantum computation can be performed within the ground state of a topologically ordered quantum system, which is a naturally protected quantum memory. In particular, we show how this can be achieved using brane-net condensates in 3-colexes. The universal set of gates is implemented without selective addressing of physical qubits and, being fully topologically protected, it does not rely on quasiparticle excitations or their braiding.Comment: revtex4, 4 pages, 4 figure

Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study

We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the similarities and differences between these two types of stabilizer codes. We compute the error correcting rate $C:=n/d^2$ for surface codes $C_s$ and color codes $C_c$ in several instances. On the torus, typical values are $C_s=2$ and $C_c=3/2$, but we find that the optimal values are $C_s=1$ and $C_c=9/8$. For planar codes, a typical value is $C_s=2$, while we find that the optimal values are $C_s=1$ and $C_c=3/4$. In general, a color code encodes twice as much logical qubits as a surface code does.Comment: revtex, 6 pages, 7 figure

Positive current noise cross-correlations in capacitively coupled double quantum dots with ferromagnetic leads

We examine cross-correlations (CCs) in the tunneling currents through two parallel interacting quantum dots coupled to four independent ferromagnetic electrodes. We find that when either one of the two circuits is in the parallel configuration with sufficiently strong polarization strength, a new mechanism of dynamical spin blockade, i.e., a spin-dependent bunching of tunneling events, governs transport through the system together with the inter-dot Coulomb interaction, leading to a sign-reversal of the zero-frequency current CC in the dynamical channel blockade regime, and to enhancement of positive current CC in the dynamical channel anti-blockade regimes, in contrast to the corresponding results for the case of paramagnetic leads.Comment: 9 pages, 3 figure

Shot noise measurements in NS junctions and the semiclassical theory

We present a new analysis of shot noise measurements in normal metal-superconductor (NS) junctions [X. Jehl et al., Nature 405, 50 (2000)], based on a recent semiclassical theory. The first calculations at zero temperature assuming quantum coherence predicted shot noise in NS contacts to be doubled with respect to normal contacts. The semiclassical approach gives the first opportunity to compare data and theory quantitatively at finite voltage and temperature. The doubling of shot noise is predicted up to the superconducting gap, as already observed, confirming that phase coherence is not necessary. An excellent agreement is also found above the gap where the noise follows the normal case.Comment: 2 pages, revtex, 2 eps figures, to appear in Phys. Rev.

Topology induced anomalous defect production by crossing a quantum critical point

We study the influence of topology on the quench dynamics of a system driven across a quantum critical point. We show how the appearance of certain edge states, which fully characterise the topology of the system, dramatically modifies the process of defect production during the crossing of the critical point. Interestingly enough, the density of defects is no longer described by the Kibble-Zurek scaling, but determined instead by the non-universal topological features of the system. Edge states are shown to be robust against defect production, which highlights their topological nature.Comment: Phys. Rev. Lett. (to be published

Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates

We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction

The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations