Condensed Matter Theory

Abstract:

We use numerical simulations and linear stability analysis to study active nematic droplets in the regime where the passive phase is isotropic. We show that activity leads to the emergence of nematic order and of spontaneous rotation in both two and three dimensions. In two dimensions the rotation is caused by the formation of a chiral +1 defect at the center of the drop. With increasing activity, the droplet deforms to an ellipse and then to a rotating annulus. Growing droplets form extended active arms which loop around to produce holes. In three dimensions the rotation is due to a disclination which loops away from and back to the surface, defining the rotation axis. In the bulk the disclination loop ends at a skyrmion. Active extensile flows deform the droplet to an oblate ellipsoid and contractile flows elongate it along the rotation axis. We compare our results on rotation in two-dimensional droplets with experiments on microtubule and motor protein suspensions and find a critical radius approximately equal to 700µm, above which the spontaneous rotation gives way to active turbulence. Comparing the simulation parameters with experiments on epithelial cell colonies shows that the crossover radius for cell colonies could be as large as 2mm, in agreement with experiments.

Abstract:

In this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as “higher-lattice gauge theory.” Higher-lattice gauge theory has so-called “2-gauge fields” describing the parallel transport of lines, in addition to ordinary 1-gauge fields which describe the parallel transport of points. In this series we explicitly construct the creation operators for the pointlike and looplike excitations supported by the model. We use these creation operators to examine the properties of the excitations, including their braiding statistics. These creation operators also reveal that some of the excitations are confined, costing energy to separate that grows linearly with the length of the creation operator used. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to rederive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground-state degeneracy on the 3-torus is related to the number of types of linked looplike excitations. This first paper provides an accessible summary of our findings, with more detailed results and proofs to be presented in the other papers in the series.