Unwinding of a one-dimensional topological superconductor

We show that a topological superconductor made of four chains of superconducting spinless fermions characterized by four Majorana edge states can adiabatically be deformed into a trivial band insulator. To unwind this time-reversal invariant topological superconductor, interactions to spinful fermions are switched on along an adiabatic path. Thereby, we couple modes which belong to two different representations of the time-reversal symmetry operator T with T^2 = 1 and T^2 = -1, respectively. This observation can be understood by investigating how the relevant symmetries act on the entanglement spectrum giving rise to four instead of eight different topological phases with Majorana edge modes. We also show that a simple level crossing of doubly and singly degenerate states occurs in the entanglement spectrum upon deforming the quantum state.Comment: 7 pages, substantial changes in the semantics compared to first versio

Random Field effects in field-driven quantum critical points

We investigate the role of disorder for field-driven quantum phase transitions of metallic antiferromagnets. For systems with sufficiently low symmetry, the combination of a uniform external field and non-magnetic impurities leads effectively to a random magnetic field which strongly modifies the behavior close to the critical point. Using perturbative renormalization group, we investigate in which regime of the phase diagram the disorder affects critical properties. In heavy fermion systems where even weak disorder can lead to strong fluctuations of the local Kondo temperature, the random field effects are especially pronounced. We study possible manifestation of random field effects in experiments and discuss in this light neutron scattering results for the field riven quantum phase transition in CeCu_5.8Au_0.2.Comment: 8 page

The Floquet-Boltzmann equation

Periodically driven quantum systems can be used to realize quantum pumps, ratchets, artificial gauge fields and novel topological states of matter. Starting from the Keldysh approach, we develop a formalism, the Floquet-Boltzmann equation, to describe the dynamics and the scattering of quasiparticles in such systems. The theory builds on a separation of time-scales. Rapid, periodic oscillations occurring on a time scale $T_0=2 \pi/\Omega$, are treated using the Floquet formalism and quasiparticles are defined as eigenstates of a non-interacting Floquet Hamiltonian. The dynamics on much longer time scales, however, is modelled by a Boltzmann equation which describes the semiclassical dynamics of the Floquet-quasiparticles and their scattering processes. As the energy is conserved only modulo $\hbar \Omega$, the interacting system heats up in the long-time limit. As a first application of this approach, we compute the heating rate for a cold-atom system, where a periodical shaking of the lattice was used to realize the Haldane model.Comment: 12 pages + 3 pages of appendix, 13 figure

Equilibration and Approximate Conservation Laws: Dipole Oscillations and Perfect Drag of Ultracold Atoms in a Harmonic Trap

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\delta\omega$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by inter-species interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of inter-species interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\tau \propto (\delta\omega)^2/\Gamma$, where $\Gamma$ is a single particle scattering rate.Comment: 9 pages + 5 pages of appendix, 9 figures; changes in v2: updated citation

Directed motion of doublons and holes in periodically driven Mott insulators

Periodically driven systems can lead to a directed motion of particles. We investigate this ratchet effect for a bosonic Mott insulator where both a staggered hopping and a staggered local potential vary periodically in time. If driving frequencies are smaller than the interaction strength and the density of excitations is small, one obtains effectively a one-particle quantum ratchet describing the motion of doubly occupied sites (doublons) and empty sites (holes). Such a simple quantum machine can be used to manipulate the excitations of the Mott insulator. For suitably chosen parameters, for example, holes and doublons move in opposite direction. To investigate whether the periodic driving can be used to move particles "uphill", i.e., against an external force, we study the influence of a linear potential $- g x$. For long times, transport is only possible when the driving frequency $\omega$ and the external force $g$ are commensurate, $n_0 g = m_0 \omega$, with $\frac{n_0}{2},m_0 \in \mathbb{Z}$.Comment: 11 pages, 9 figure

Capturing of a Magnetic Skyrmion with a Hole

Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an unpinned skyrmion moves around the impurities and never gets captured. For higher current densities, j_c1 < j < j_c2, however, single holes are able to capture moving skyrmions. The maximal cross section is proportional to the skyrmion radius and to Sqrt(alpha), where alpha is the Gilbert damping. For j > j_c2 all skyrmions are depinned. Small changes of the magnetic field strongly change the pinning properties, one can even reach a regime without pinning, j_c2=0. We also show that a small density of holes can effectively accelerate the motion of the skyrmion and introduce a Hall effect for the skyrmion.Comment: 11 page

Dynamics and energetics of emergent magnetic monopoles in chiral magnets

The formation and destruction of topologically quantized magnetic whirls, so-called skyrmions, in chiral magnets is driven by the creation and motion of singular hedgehog defects. These can be identified with emergent magnetic monopoles and antimonopoles. We investigate how the energetics of and forces between monopoles and antimonopoles influence their creation rate and dynamics. We study a single skyrmion line defect in the helical phase using both micromagnetic simulations and a Ginzburg-Landau analysis. Monopole-antimonople pairs are created in a thermally activated process, largely controlled by the (core) energy of the monopole. The force between monopoles and antimonopoles is linear in distance and described by a string tension. The sign and size of the string tension determines the stability of the phases and the velocity of the monopoles.Comment: 4 pages, 5 figure

Quench dynamics and statistics of measurements for a line of quantum spins in two dimensions

Motivated by recent experiments, we investigate the dynamics of a line of spin-down spins embedded in the ferromagnetic spin-up ground state of a two-dimensional xxz model close to the Ising limit. In a situation where the couplings in x and y direction are different, the quench dynamics of this system is governed by the interplay of one-dimensional excitations (kinks and holes) moving along the line and single-spin excitations evaporating into the two-dimensional background. A semiclassical approximation can be used to calculate the dynamics of this complex quantum system. Recently, it became possible to perform projective quantum measurements on such spin systems, allowing to determine, e.g., the z-component of each individual spin. We predict the statistical properties of such measurements which contain much more information than correlation functions.Comment: 10 pages, 7 figure