Crystallization of the resonating valence bond liquid as vortex condensation

We show that the liquid-to-crystal quantum phase transition in the Rokhsar-Kivelson dimer model on the two-dimensional triangular lattice occurs as a condensation of vortexlike excitations called "visons." This conclusion is drawn from numerical studies of the vison spectrum in the liquid phase by using the Green's function Monte Carlo method. We find that visons remain the lowest excitation throughout the liquid phase and that their gap decreases continuously to zero at the phase transition. The nature of the crystal phase and the second order of the phase transition are in agreement with an earlier prediction of Moessner and Sondhi.

Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase

Marco Cantoni, Fabrizio Carbone, Ping Huang, Arnaud Magrez, Henrik Moodysson Rønnow, Thomas Schönenberger

While in 3D materials melting is a single, first-order phase transition, in 2D systems, it can also proceed via an intermediate phase. For a skyrmion lattice in Cu2OSeO3, magnetic field variations can tune this quasiparticle 2D solid into a skyrmion liquid via an intermediate hexatic phase with short-range translational and quasi-long-range orientational order. The phase transition most commonly observed is probably melting, a transition from ordered crystalline solids to disordered isotropic liquids. In three dimensions, melting is a single, first-order phase transition. In two-dimensional systems, however, theory predicts a general scenario of two continuous phase transitions separated by an intermediate, oriented liquid state, the so-called hexatic phase with short-range translational and quasi-long-range orientational orders. Such hexatic phases occur in colloidal systems, Wigner solids and liquid crystals, all composed of real-matter particles. In contrast, skyrmions are countable soliton configurations with non-trivial topology and these quasi-particles can form two-dimensional lattices. Here we show, by direct imaging with cryo-Lorentz transmission electron microscopy, that magnetic field variations can tune the phase of the skyrmion ensembles in Cu(2)OSeO(3)from a two-dimensional solid through the long-speculated skyrmion hexatic phase to a liquid. The local spin order persists throughout the process. Remarkably, our quantitative analysis demonstrates that the aforementioned topological-defect-induced crystal melting scenario well describes the observed phase transitions.

NATURE PUBLISHING GROUP2020

The Scrambled Net Filter

Thomas Gsponer

The standard Kalman filter is a powerful and widely used tool to perform prediction, filtering and smoothing in the fields of linear Gaussian state-space models. In its standard setting it has a simple recursive form which implies high computational efficiency. As the latter is essentially a least squares procedure optimality properties can be derived easily. These characteristics of the standard Kalman filter depend strongly on distributional and linearity assumptions of the model. If we consider nonlinear non-Gaussian state-space models all these properties and characteristics are no longer valid. Consequently there are different approaches on the robustification of the Kalman filter. One is based on the the ideas of minimax problems and influence curves. Others use numerical integration and Monte Carlo methods. Herein we propose a new filter by implementing a method of numerical integration, called scrambled net quadrature, which consists of a mixture of Monte Carlo methods and quasi-Monte Carlo methods, providing an integration error of order of magnitude