Abstract
We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for large N, we find that the net defect number variance in convex volumina scales as the surface area of the sample for short-range correlations. This behaviour follows generally from spatial and internal symmetries. Conversely, if spatial isotropy is broken, e.g. by a lattice, and in addition long-range periodic correlations develop in the broken-symmetry phase, we get the rather counterintuitive result that the scaling strongly depends on the dimension being even or odd: for even dimensions, the net defect number variance scales as the surface area squared, with a prefactor oscillating with the system size, while for odd dimensions, it essentially vanishes.
Highlights
Sweeping through a second-order symmetry-breaking phase transition in general may trigger the creation of topological defects
The fundamental global requirement for topological defect generation is that the symmetry group of the new phase permits the defects in the sense that the homotopy group of the coset space, formed by the quotient space of unbroken and broken symmetries is nontrivial
While Kibble realized that in the early universe relativistic causality alone mandates the appearance of defects according to the nontrivial homotopy groups relevant to the symmetrybreaking scheme at hand, Zurek used scalings of the relaxation time and healing length with the quench time in the vicinity of the critical point to predict topological defect densities
Summary
Sweeping through a second-order (quantum or thermal) symmetry-breaking phase transition in general may trigger the creation of topological defects. A clean experimental evidence for Kibble-Zurek mediated defect formation in dilute cold atomic gases, which are an experimentally precisely in situ controllable variant of conventional condensed matter systems, has been obtained in spinor as well as scalar Bose gases [24, 25] These dilute gases are suitable to test predictions of the dynamical Kibble-Zurek theory because of their comparatively long re-equilibration times, which effectively permit a real-time study of the evolution of perturbations in the spatial many-body correlations and a study of the creation process of topological defects. We begin by deriving a large N expansion for a general O(N ) model resulting in a bilinear effective action, which is used to obtain the equations of motion describing the instability of direction modes during the phase transition We apply these equations to calculate the behavior of the spatial direction correlation functions shortly after the transition. We delineate the behavior of the winding number variance with the size of the sample in dependence on the spatial behavior of the direction correlations (which is, e.g., short-range or long-range periodic)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
