V. R. Vieira

Path integrals of spin-J systems in the holomorphic representation

Abstract A path integral expression for the matrix element and the diagonal representative of the spin- J evolution operator or Boltzmann factor is obtained using Bloch coherent states in the holomorphic representation, yielding the appropriate boundary conditions. Quantum Dyson-Schwinger equations of motion are derived and used as criteria to select the appropriate action. In the case of the diagonal representative the equations of motion satisfy the commutation relations of the spin operators and are the classical limit of the Dyson-Schwinger equations, if we redefine the Lagrangian together with the integration measure. It is shown that in the case of a spin in a time-independent magnetic field the saddle-point approximation for both representatives gives the exact results. We present analytical algorithms to obtain the exponential factor and the prefactor in the saddle-point expansion, without an ad hoc reduction to an effective one-dimensional problem, but keeping instead a 2 × 2 matrix structure. We apply our results to several models.

Fidelity between partial states as a signature of quantum phase transitions

We introduce a partial state fidelity approach to quantum phase transitions. We consider a superconducting lattice with a magnetic impurity inserted at its center, and look at the fidelity between partial (either one-site or two-site) quantum states. In the vicinity of the point of the quantum phase transition, we observe a sudden drop of the fidelity between two one-site partial states corresponding either to the impurity location or its close vicinity. This enables us to identify the on-site magnetization as the order parameter for the phase transition studied. In the case of two-site states, the fidelity reveals the transition point as long as one of the two electron sites is located at the impurity, while the other lies elsewhere in the lattice. We also determine the Uhlmann mixed state geometric phase, recently introduced in the study of the structural change of the system state eigenvectors in the vicinity of the lines of thermal phase transitions, and find it to be trivial, both for one- and two-site partial states, except when an electron site is at the impurity. This means that the system partial state eigenvectors do not contribute significantly to the enhanced state distinguishability around the point of this quantum phase transition. Finally, we use the fidelity to analyze the total amount of correlations contained within a composite system, showing that, even for the smallest one-site states, it features an abrupt quantitative change in the vicinity of the point of the quantum phase transition.

Entanglement controlled single-electron transmittivity

We show that the electron transmittivity of single electrons propagating along a one-dimensional (1D) wire in the presence of two magnetic impurities is affected by the entanglement between the impurity spins. For suitable values of the electron wave vector, there are two maximally entangled spin states which, respectively, make the wire completely transparent whatever the electron spin state or strongly inhibit electron transmission.

Current-induced motion of a domain wall in a magnetic nanowire

The dynamics of current-induced motion of a magnetic domain wall in a quasi-one-dimensional ferromagnet with both easy-axis and easy-plane anisotropy, is studied. We pay a special attention to the case of a sharp domain wall, and calculate the spin torque created by the electric current. The torque has two components, one of which is acting as a driving force for the motion of the domain wall while the other distorts its shape, forcing thus the magnetic moments to deviate from the easy plane.

Electron Fabry–Perot interferometer with two entangled magnetic impurities

We consider a one-dimensional (1D) wire along which single conduction electrons can propagate in the presence of two spin-1/2 magnetic impurities. The electron may be scattered by each impurity via a contact-exchange interaction and thus a spin-flip generally occurs at each scattering event. Adopting a quantum waveguide theory approach, we derive the stationary states of the system at all orders in the electron–impurity exchange coupling constant. This allows us to investigate electron transmission for arbitrary initial states of the two impurity spins. We show that for suitable electron wave vectors, the triplet and singlet maximally entangled spin states of the impurities can respectively largely inhibit the electron transport or make the wire completely transparent for any electron spin state. In the latter case, a resonance condition can always be found, representing an anomalous behaviour compared to typical decoherence induced by magnetic impurities. We provide an explanation for these phenomena in terms of the Hamiltonian symmetries. Finally, a scheme to generate maximally entangled spin states of the two impurities via electron scattering is proposed.

Uhlmann Connection in Fermionic Systems Undergoing Phase Transitions

We study the behavior of the Uhlmann connection in systems of fermions undergoing phase transitions. In particular, we analyze some of the paradigmatic cases of topological insulators and superconductors in one dimension, as well as the BCS theory of superconductivity in three dimensions. We show that the Uhlmann connection signals phase transitions in which the eigenbasis of the state of the system changes. Moreover, using the established fidelity approach and the study of the edge states, we show the absence of thermally driven phase transitions in the case of topological insulators and superconductors. We clarify what is the relevant parameter space associated with the Uhlmann connection so that it signals the existence of order in mixed states. In addition, the study of Majorana modes at finite temperature opens the possibility of applications in realistic stable quantum memories. Finally, the analysis of the different behavior of the BCS model and the Kitaev chain, with respect to the Uhlmann connection, suggested that in realistic scenarios the gap of topological superconductors could also, generically, be temperature dependent.

Entanglement between nitrogen vacancy spins in diamond controlled by a nanomechanical resonator

We suggest a new type of nano-electromechanical resonator, the functionality of which is based on a magnetic field induced deflection of an appropriate cantilever that oscillates between nitrogen vacancy (NV) spins in daimond. Specifically, we consider a Si(100) cantilever coated with a thin magnetic Ni film. Magnetoelastic stress and magnetic-field induced torque are utilized to induce a controlled cantilever deflection. It is shown that, depending on the value of the system parameters, the induced asymmetry of the cantilever deflection substantially modifies the characteristics of the system. In particular, the coupling strength between the NV spins and the degree of entanglement can be controlled through magnetoelastic stress and magnetic-field induced torque effects. Our theoretical proposal can be implemented experimentally with the potential of increasing several times the coupling strength between the NV spins as compared to the maximal coupling strength reported before in P. Rabl, et al. Phys. Rev. B 79, 041302(R) (2009).

Superconductivity in the SU ( N ) Anderson lattice at U

We present a mean-field study of superconductivity in a generalized N-channel cubic Anderson lattice at U=\infty taking into account the effect of a nearest-neighbor attraction J. The condition U=\infty is implemented within the slave-boson formalism considering the slave bosons to be condensed. We consider the

Quantum information and phase transitions: Fidelity and state distinguishability

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Macroscopic distinguishability between quantum states defining different phases of matter: fidelity and the Uhlmann geometric phase.

-level occupancy ranging from the mixed valence regime to the Kondo limit and study the dependence of the critical temperature on the various model parameters for each of three possible Cooper pairing symmetries (extended s, d-wave and p-wave pairing) and find interesting crossovers. It is found that the d- and p- wave order parameters have, in general, very similar critical temperatures. The extended s-wave pairing seems to be relatively more stable for electronic densities per channel close to one and for large values of the superconducting interaction J.