Seminar on the Theory of Complex Systems  Summer Term 2015

Chiral magnets support topological skyrmion textures due to the Dzyaloshinskii-Moriya spin-orbit interaction. After an introduction to the topic, we discuss the interaction between such a magnetic skyrmion and its small-amplitude fluctuations, i.e., the magnons in a two-dimensional chiral magnet. The magnon spectrum includes two magnon-skyrmion bound states corresponding to a breathing mode and, for intermediate fields, a quadrupolar mode, which will give rise to subgap magnetic and electric resonances. Due to the skyrmion topology, the magnons scatter from an emergent flux density that leads to skew and rainbow scattering, characterized by an asymmetric and oscillating differential cross section. As a consequence of the skew scattering, a finite density of skyrmions will generate a topological magnon Hall effect. Using the conservation law for the energy-momentum tensor, we demonstrate that the magnons also transfer momentum to the skyrmion. As a consequence, a magnon current leads to magnon pressure reflected in a momentum-transfer force in the Thiele equation of motion for the skyrmion. This force is reactive and governed by the transport scattering cross sections of the skyrmion; it causes not only a finite skyrmion velocity but also a large skyrmion Hall effect. While at small energies the transversal momentum transfer is negligible resulting in a large skyrmion Hall angle, we demonstrate that it dominates in the limit of high-energies leading to a universal relation between the magnon current and the skyrmion velocity.

1. C. Schuette and M. Garst, Phys. Rev. B 90, 094423 (2014)
2. S. Schroeter and M. Garst, arXiv:1504.02108

Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood quantum statistical effects, the coherent superposition of many-particle amplitudes rapidly overburdens classical computing devices - essentially by creating extremely complicated interference patterns. With the advent of controlled many-particle interference experiments, optical set-ups that can efficiently probe many-boson wave functions - baptised BosonSamplers - have therefore been proposed as efficient quantum simulators which outperform any classical computing device. However, as in all experimental quantum simulations of truly complex systems, there remains one crucial problem: How to certify that a given experimental measurement record is an unambiguous result of sampling bosons rather than fermions or distinguishable particles, or of uncontrolled noise? We describe and quantify a statistical signature of many-body quantum interference, which can be used as an experimental (and classically computable) benchmark for BosonSampling.