Search

We present a novel theoretical approach to incorporate electronic interactions in the study of two-dimensional topological insulators. By exploiting the correspondence between edge state physics and entanglement spectrum in gapped topological systems, we deconstruct the system into one-dimensional channels. This framework enables a simple and elegant inclusion of fermionic interactions into the discussion of topological insulators. We apply this approach to the Kane-Mele model with interactions and magnetic impurities., Comment: 5 pages, 3 figures; added reference; corrected typos; improved discussions

We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature -- we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent., Comment: 18 pages. Accepted version: small corrections and improvements from v1

Skyrmions are emerging topological spin structures that are potentially revolutionary for future data storage and spintronics applications. The existence and stability of skyrmions in magnetic materials is usually associated to the presence of the Dzyaloshinskii-Moriya interaction (DMI) in bulk magnets or in magnetic thin films lacking inversion symmetry. While some methods have already been proposed to generate isolated skyrmions in thin films with DMI, a thorough study of the conditions under which the skyrmions will remain stable in order to be manipulated in an integrated spintronic device are still an open problem. The stability of such structures is believed to be a result of ideal combinations of perpendicular magnetic anisotropy (PMA), DMI and the interplay between geometry and magnetostatics. In the present work we show some micromagnetic results supporting previous experimental observations of magnetic skyrmions in spin-valve stacks with a wide range of DMI values. Using micromagnetic simulations of cobalt-based disks, we obtain the magnetic ground state configuration for several values of PMA, DMI and geometric parameters. Skyrmion numbers, corresponding to the topological charge, are calculated in all cases and confirm the occurrence of isolated, stable, axially symmetric skyrmions for several combinations of DMI and anisotropy constant. The stability of the skyrmions in disks is then investigated under magnetic field and spin-polarized current, in finite temperature, highlighting the limits of applicability of these spin textures in spintronic devices., Comment: 26 pages, 13 figures

We study the long-time evolution of a quantum memory coupled to a bosonic environment on which quantum error correction (QEC) is performed using the surface code. The memory's evolution encompasses $N$ QEC cycles, each of them yielding a non-error syndrome. This assumption makes our analysis independent of the recovery process. We map the expression for the time evolution of the memory onto the partition function of an equivalent statistical mechanical spin system. In the superohmic dissipation case the long-time evolution of the memory has the same behavior as the time evolution for just one QEC cycle. For this case we find analytical expressions for the critical parameters of the order-disorder phase transition of an equivalent spin system. These critical parameters determine the threshold value for the system-environment coupling below which it is possible to preserve the memory's state., Comment: 8 pages, 2 figures

We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered: super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant to current experiments, quantum error correction works well even in the presence of environment-induced, long-range inter-qubit interactions. A threshold always exists at finite temperatures, although its temperature dependence is very sensitive to the type of environment. For the super-Ohmic case, the critical coupling constant separating high- from low-fidelity decreases with increasing temperature. For both Ohmic and super-Ohmic cases, the dependence of the critical coupling on temperature is weak. In all cases, the critical coupling is determined by microscopic parameters of the environment. For the sub-Ohmic case, it also depends strongly on the duration of the QEC cycle., Comment: 13 pages, 6 figures

Magnetic vortex cores exhibit a gyrotropic motion, and may reach a critical velocity, at which point they invert their z-component of the magnetization. We performed micromagnetic simulations to describe this vortex core polarity reversal in magnetic nanodisks presenting a perpendicular anisotropy. We found that the critical velocity decreases with increasing perpendicular anisotropy, therefore departing from a universal criterion, that relates this velocity only to the exchange stiffness of the material. This leads to a critical velocity inversely proportional to the vortex core radius. We have also shown that in a pair of interacting disks, it is possible to switch the core vortex polarity through a non-local excitation; exciting one disk by applying a rotating magnetic field, one is able to switch the polarity of a neighbor disk, with a larger perpendicular anisotropy.

The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We develop an exact formulation for the fidelity of the surface code that allows us to probe much further on this promise of strong protection. This formulation goes beyond the stochastic single-qubit error model approximation and can take into account both correlated errors and inhomogeneities in the coupling between physical qubits and the environment. For the case of a bit-flipping environment, we map the complete evolution after one quantum error correction cycle onto the problem of computing correlation functions of a two-dimensional Ising model with boundary fields. Exact results for the fidelity threshold of the surface code are then obtained for several relevant types of noise. Analytical predictions for a representative case are confirmed by Monte Carlo simulations., Comment: 12 pages, 6 figures; revised and extended version

Interacting magnetic nanoobjects constitute one key component for many proposed spintronic devices, from microwave nano-oscillators to magnetic memory elements. For this reason, the mechanism of this interaction and its dependence with distance $d$ between these nanoobjects has been the subject of several recent studies. In the present work, the problem of the interaction between magnetic nanodisks with magnetic vortex structures is treated both analytically and through micromagnetic simulation. The coupling of two magnetic nanodisks is obtained, in the case of nanodisks with different gyrotropic frequencies. The motion of the two vortex cores, and consequently the time dependence of the total magnetization $M(t)$ is derived using Thiele's equation and by simulation. The magnetic coupling strength as a function of the distance between the disks of each pair is computed with a recently developed method, using the magnetic vortex echoes, analogous to the NMR spin echoes. The results of the two approaches differ by approximately $10\%$ and can be fitted with a multipolar expansion of odd negative powers of $d$; using one single term, a dependence with distance found is broadly in agreement with studies employing other techniques. The coupling frequencies as a function of distance for the pair of nonidentical disks are also obtained., Comment: 6 pages, 5 figures. This is version 2 of the manuscript where figure 1 has been replaced due to typing erros. Figures 4 and 5 have also been replaced to reflect a better fitting procedure

The magnetic vortex structure, that is present in several nanoscopic systems, is stable and can be manipulated through the application of a magnetic field or a spin polarized current. The size and shape of the core are strongly affected by the anisotropy, however its role on the core behavior has not yet been clarified. In the present work we investigate the influence of a perpendicular anisotropy on the annihilation and shape of magnetic vortex cores in permalloy disks. We have used both micromagnetic simulations with the OOMMF code, and an analytical model that assumes that the shape of the core does not change during the hysteresis cycle, known as the rigid core model, to calculate the annihilation fields. In both cases we found that the annihilation fields decrease with increasing perpendicular anisotropy for almost all the structures investigated. The simulations show that for increasing anisotropy or dot thickness, or both, the vortex core profile changes its shape, becoming elongated. For every dot thickness, this change does not depend on the dot radius, but on the relative distance of the core from the center of the dot., Comment: 7 pages and 9 figures

We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation allows us to map the problem onto an Ising-like statistical spin model with two-body interactions and a fictitious temperature which is related to the inverse bath coupling constant. The model departs from the usual Ising model in the sense that interactions can be long ranged and can involve complex exchange couplings; in addition, the number of allowed configurations is restricted by the syndrome extraction. Using analytical estimates and numerical calculations, we argue that, in the limit of an infinite number of physical qubits, the spin model sustain a phase transition which can be associated to the existence of an error threshold in the surface code. An estimate of the transition point is given for the case of nearest-neighbor interactions., Comment: 15 pages, 5 figures

We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors., Comment: 5 pages, 2 figures

We propose the use of the gyrotropic motion of vortex cores in nanomagnets to produce a magnetic echo, analogous to the spin echo in NMR. This echo occurs when an array of nanomagnets, e.g., nanodisks, is magnetized with an in-plane (xy) field, and after a time \tau a field pulse inverts the core magnetization; the echo is a peak in M_{xy} at t=2\tau. Its relaxation times depend on the inhomogeneity, on the interaction between the nanodots and on the Gilbert damping constant \alpha. Its feasibility is demonstrated using micromagnetic simulation. To illustrate an application of the echoes, we have determined the inhomogeneity and measured the magnetic interaction in an array of nanodisks separated by a distance d, finding a d^{-n} dependence, with n\approx 4., Comment: 4 pages, with 4 figures

Nanodots with magnetic vortices have many potential applications, such as magnetic memories (VRAMs) and spin transfer nano-oscillators (STNOs). Adding a perpendicular anisotropy term to the magnetic energy of the nanodot it becomes possible to tune the vortex core properties. This can be obtained, e.g., in Co nanodots by varying the thickness of the Co layer in a Co/Pt stack. Here we discuss the spin configuration of circular and elliptical nanodots for different perpendicular anisotropies; we show for nanodisks that micromagnetic simulations and analytical results agree. Increasing the perpendicular anisotropy, the vortex core radii increase, the phase diagrams are modified and new configurations appear; the knowledge of these phase diagrams is relevant for the choice of optimum nanodot dimensions for applications. MFM measurements on Co/Pt multilayers confirm the trend of the vortex core diameters with varying Co layer thicknesses., Comment: 7 pages, 8 figures

We obtain an upper bound on the time available for quantum computation for a given quantum computer and decohering environment with quantum error correction implemented. First, we derive an explicit quantum evolution operator for the logical qubits and show that it has the same form as that for the physical qubits but with a reduced coupling strength to the environment. Using this evolution operator, we find the trace distance between the real and ideal states of the logical qubits in two cases. For a super-Ohmic bath, the trace distance saturates, while for Ohmic or sub-Ohmic baths, there is a finite time before the trace distance exceeds a value set by the user., Comment: 4 pages (revised title, following PRA request)

Magnetic disks or dots of soft magnetic material of sub-micron dimensions may have as the lowest energy magnetic configuration a single-domain structure, with magnetization either perpendicular of parallel to the plane, or else may form magnetic vortices. The properties of these vortices may be used to encode data bits, in magnetic memory applications. In the present work the OOMMF code was used to compute by micromagnetic simulation the energy and the magnetization of circular and elliptical nanodots of permalloy. For the elliptical magnetic dots the analysis was made for variable thickness and length of major axis, keeping a 2:1 axis ratio. From the simulations, a phase diagram was constructed, where the ground state configurations of the nanodots are represented in a diagram of nanodot height versus length of the major axis $2a$ of the ellipse. The phase diagram obtained includes regions with one and two vortices; it is similar, but more complex than that derived using a numerical scaling approach, since it includes configurations with lateral vortices. These diagrams are useful as guides for the choice of dimensions of elliptical nanodots for practical applications., Comment: 8 pages, 5 figures

We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is indeed possible, we find formal expressions for the probability of a faulty path and the residual decoherence encoded in the reduced density matrix. Systems with non-zero gate times (``long gates'') are included in our analysis by using an upper bound on the noise. In order to introduce the local error probability for a qubit, we assume that propagation of signals through the environment is slower than the QEC period (hypercube assumption). This allows an explicit calculation in the case of a generalized spin-boson model and a quantum frustration model. The key result is a dimensional criterion: If the correlations decay sufficiently fast, the system evolves toward a stochastic error model for which the threshold theorem of fault-tolerant quantum computation has been proven. On the other hand, if the correlations decay slowly, the traditional proof of this threshold theorem does not hold. This dimensional criterion bears many similarities to criteria that occur in the theory of quantum phase transitions., Comment: 19 pages, 5 figures. Includes response to arXiv:quant-ph/0702050. New title and an additional example

We analyze the problem of a quantum computer in a correlated environment protected from decoherence by QEC using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of the computer and the scaling dimension of the correlations. For an irrelevant flow, the error probability is reduced to a stochastic form for long time and/or large number of qubits; thus, the traditional derivation of the threshold theorem holds for these error models. In this way, the ``threshold theorem'' of quantum computing is rephrased as a dimensional criterion., Comment: 4.1 pages, minor correction and an improved discussion of Eqs. (4) and (14)

We study the decoherence of a quantum computer in an environment which is inherently correlated in time and space. We first derive the nonunitary time evolution of the computer and environment in the presence of a stabilizer error correction code, providing a general way to quantify decoherence for a quantum computer. The general theory is then applied to the spin-boson model. Our results demonstrate that effects of long-range correlations can be systematically reduced by small changes in the error correction codes., Comment: 4 pages, 1 figure, Phys. Rev. Lett. in press

We study a model of frustration of decoherence in an open quantum system. Contrary to other dissipative ohmic impurity models, such as the Kondo model or the dissipative two-level system, the impurity model discussed here never presents overdamped dynamics even for strong coupling to the environment. We show that this unusual effect has its origins in the quantum mechanical nature of the coupling between the quantum impurity and the environment. We study the problem using analytic and numerical renormalization group methods and obtain expressions for the frequency and temperature dependence of the impurity susceptibility in different regimes., Comment: 14 pages, 5 figures

The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight-biding regime. For the case of half flux per plaquette, and for a wide range of values of the dissipation, the physics of the model is determined by a non trivial fixed point. A combination of exact and variational results is used to characterize this fixed point. Finally, it is also argued that there is an intermediate energy scale that separates the weak coupling physics from the tight-binding solution., Comment: 4 pages 3 figures

We analyze a quantum computer (QC) design based on nuclear spin qubits in a quasi-one-dimensional (1D) chain of non-Kramers doublet atoms. We explore the use of spatial symmetry breaking to obtain control over the local dynamics of a qubit. We also study the decoherence mechanisms at the single qubit level and the interactions mediated by the magnetic media. The design can be realized in $\textrm{PrBr}_{\textrm{3}-x}\textrm{F}_{x}$ with nuclear magnetic resonance (NMR) techniques., Comment: 7 pages, 3 figures

We discuss the problem of a spin 1/2 impurity immersed in a spin S magnetically ordered background. We show that the problem maps onto a generalization of the dissipative two level system (DTLS) with two independent heat baths, associated with the Goldstone modes of the magnet, that couple to different components of the impurity spin operator. Using analytical perturbative renormalization group (RG) methods and accurate numerical renormalization group (NRG) we show that contrary to other dissipative models there is quantum frustration of decoherence and quasi-scaling even in the strong coupling regime. We make predictions for the behavior of the impurity magnetic susceptibility that can be measured in nuclear magnetic resonance (NMR) experiments. Our results may also have relevance to quantum computation., Comment: 4 pages, 3 figures

We study the one-dimensional Kondo lattice model through the density matrix renormalization group (DMRG). Our results for the spin correlation function indicate the presence of a small Fermi surface in large portions of the phase diagram, in contrast to some previous studies that used the same technique. We argue that the discrepancy is due to the open boundary conditions, which introduce strong charge perturbations that strongly affect the spin Friedel oscillations., Comment: 5 pages, 7 figures

We establish a mapping of a general spin-fermion system in one dimension into a classical generalized Coulomb gas. This mapping allows a renormalization group treatment of the anisotropic Kondo chain both at and away from half-filling. We find that the phase diagram contains regions of paramagnetism, partial and full ferromagnetic order. We also use the method to analyze the phases of the Ising-Kondo chain., Comment: 19 pages, 9 figures

We establish the phase diagram of the one-dimensional anisotropic Kondo lattice model at T=0 using a generalized two-dimensional classical Coulomb gas description. We analyze the problem by means of a renormalization group (RG) treatment. We find that the phase diagram contains regions of paramagnetism, partial and full ferromagnetic order., Comment: Final version to appear in Physical Review Letters