22 research outputs found
Skyrmion collapse
We investigate the topological change of a Belavin-Polyakov skyrmion under
the action of a spin-polarized current. The dynamics is described by the
Schr\"odinger equation for the electrons carrying the current coupled to the
Landau-Lifshitz equation for the evolution of the magnetic texture in a square
lattice. We show that the addition of an exchange dissipation term, tends to
smooth the transition from the skyrmion state to the ferromagnetic state. We
demonstrate that this topological change, in the continuum dissipationless
limit, can be described as a self-similar finite-time singularity by which the
skyrmion core collapses.Comment: 9 pages, 6 figures; v2. discussion added (the title of the published
version is "Skyrmion to ferromagnetic state transition: A description of the
topological change as a finite-time singularity in the skyrmion dynamics"
Interacting quantum walk on a graph
We introduce an elementary quantum system consisting of a set of spins on a
graph and a particle hopping between its nodes. The quantum state is build
sequentially, applying a unitary transformation that couples neighboring spins
and, at a node, the local spin with the particle. We observe the relaxation of
the system towards a stationary paramagnetic or ferromagnetic state, and
demonstrate that it is related to eigenvectors thermalization and random matrix
statistics. The relation between these macroscopic properties and interaction
generated entanglement is discussed.Comment: 15 pages, 11 figures (v2 extended version
Edge states in a two-dimensional quantum walk with disorder
We investigate the effect of spatial disorder on the edge states localized at
the interface between two topologically different regions. Rotation disorder
can localize the quantum walk if it is strong enough to change the topology,
otherwise the edge state is protected. Nonlinear spatial disorder, dependent on
the walker's state, attracts the walk to the interface even for very large
coupling, preserving the ballistic transport characteristic of the clean
regime.Comment: extended new version; 10 pages, 10 figure
Topological changes of two-dimensional magnetic textures
We investigate the interaction of magnetic vortices and skyrmions with a
spin-polarized current. In a square lattice, fixed classical spins and quantum
itinerant electrons, evolve according to the coupled Landau-Lifshitz and
Schr\"odinger equations. Changes in the topology occur at microscopic time and
length scales, and are shown to be triggered by the nucleation of a nontrivial
electron-spin structure at the vortex core.Comment: See supplementary material (high resolution figures and movies)
https://drive.google.com/folderview?id=0By4j_RJ9SKLpQ2R5UklXLURvbEE&usp=sharing
--- v2: Extended versio
Anomalous quantum Hall effect induced by disorder in topological insulators
We investigate a transition between a two-dimensional topological insulator
conduction state, characterized by a conductance (in fundamental units
) and a Chern insulator with , induced by polarized magnetic
impurities. Two kinds of coupling, ferro and antiferromagnetic, are considered
with the electron and hole subbands. We demonstrate that for strong disorder, a
phase exists even for ferromagnetic order, in contrast with the
prediction of the mean field approximation. This result is supported by direct
numerical computations using Landauer transport formula, and by analytical
calculations of the chemical potential and mass renormalization as a function
of the disorder strength, in the self-consistent Born approximation. The
transition is related to the suppression of one of the spin conduction
channels, for strong enough disorder, by selective spin scattering and
localization.Comment: 9 pages, 4 figures (figs. 2 and 3 in low resolution
Entanglement dynamics and phase transitions of the Floquet cluster spin chain
Cluster states were introduced in the context of measurement based quantum
computing. In one dimension, the cluster Hamiltonian possesses topologically
protected states. We investigate the Floquet dynamics of the cluster spin chain
in an external field, interacting with a particle. We explore the entanglement
properties of the topological and magnetic phases, first in the integrable spin
lattice case, and then in the interacting quantum walk case. We find, in
addition to thermalization, dynamical phase transitions separating low and high
entangled nonthermal states, reminiscent of the ones present in the integrable
case, but differing in their magnetic properties.Comment: 12 pages, 9 figures; comments are welcom
Quantum walk on a graph of spins: magnetism and entanglement
We introduce a model of a quantum walk on a graph in which a particle jumps
between neighboring nodes and interacts with independent spins sitting on the
edges. Entanglement propagates with the walker. We apply this model to the case
of a one dimensional lattice, to investigate its magnetic and entanglement
properties. In the continuum limit, we recover a Landau-Lifshitz equation that
describes the precession of spins. A rich dynamics is observed, with regimes of
particle propagation and localization, together with spin oscillations and
relaxation. Entanglement of the asymptotic states follows a volume law for most
parameters (the coin rotation angle and the particle-spin coupling).Comment: 50 pages, 114 references, 30 figure
Entanglement and interaction in a topological quantum walk
We study the quantum walk of two interacting particles on a line with an
interface separating two topologically distinct regions. The interaction
induces a localization-delocalization transition of the edge state at the
interface. We characterize the transition through the entanglement between the
two particles.Comment: 16 pages, 7 figures (slightly expanded version
Anisotropic dynamics of a vicinal surface under the meandering step instability
We investigate the nonlinear evolution of the Bales-Zangwill instability,
responsible for the meandering of atomic steps on a growing vicinal surface. We
develop an asymptotic method to derive, in the continuous limit, an evolution
equation for the two-dimensional step flow. The dynamics of the crystal surface
is greatly influenced by the anisotropy inherent to its geometry, and is
characterized by the coarsening of undulations along the step direction and by
the elastic relaxation in the mean slope direction. We demonstrate, using
similarity arguments, that the coalescence of meanders and the step flow follow
simple scaling laws, and deduce the exponents of the characteristic length
scales and height amplitude. The relevance of these results to experiments is
discussed.Comment: 10 pages, 7 figures; submitted to Phys. Rev.
Hamiltonian Dynamics and the Phase Transition of the XY Model
A Hamiltonian dynamics is defined for the XY model by adding a kinetic energy
term. Thermodynamical properties (total energy, magnetization, vorticity)
derived from microcanonical simulations of this model are found to be in
agreement with canonical Monte-Carlo results in the explored temperature
region. The behavior of the magnetization and the energy as functions of the
temperature are thoroughly investigated, taking into account finite size
effects. By representing the spin field as a superposition of random phased
waves, we derive a nonlinear dispersion relation whose solutions allow the
computation of thermodynamical quantities, which agree quantitatively with
those obtained in numerical experiments, up to temperatures close to the
transition. At low temperatures the propagation of phonons is the dominant
phenomenon, while above the phase transition the system splits into ordered
domains separated by interfaces populated by topological defects. In the high
temperature phase, spins rotate, and an analogy with an Ising-like system can
be established, leading to a theoretical prediction of the critical temperature
.Comment: 10 figures, Revte