Condensed Matter Theory

Abstract:

The 2 + 1 dimensional lattice models of Levin and Wen (2005) [1] provide the most general known microscopic construction of topological phases of matter. Based heavily on the mathematical structure of category theory, many of the special properties of these models are not obvious. In the current paper, we present a geometrical space-time picture of the partition function of the Levin-Wen models which can be described as doubles (two copies with opposite chiralities) of underlying anyon theories. Our space-time picture describes the partition function as a knot invariant of a complicated link, where both the lattice variables of the microscopic Levin-Wen model and the terms of the Hamiltonian are represented as labeled strings of this link. This complicated link, previously studied in the mathematical literature, and known as Chain-Mail, can be related directly to known topological invariants of 3-manifolds such as the so-called Turaev-Viro invariant and the Witten-Reshitikhin-Turaev invariant. We further consider quasi-particle excitations of the Levin-Wen models and we see how they can be understood by adding additional strings to the Chain-Mail link representing quasi-particle world-lines. Our construction gives particularly important new insight into how a doubled theory arises from these microscopic models. © 2010 Elsevier Inc.

Abstract:

We examine the possibilities to use the intrinsic 3D defect networks in blue phases I and II as arrays of trapping sites for colloidal particles. Our approach based on the phenomenological Landau-de Gennes description and topological theory has proven to be extremely useful in dealing with nematic colloids. A perturbed orientational order leads to effective anisotropic long range inter-particle coupling and consequently to numerous organizations of colloidal particles not present in simple liquids. Recent developments that led to the blue phases with extended stability range make them more attractive for use. In these phases the competition between nematic ordering and intrinsic tendency to form double twisted deformations yields complex director patterns and disclination networks. The spatially deformed order that mediates the attraction of particles to the network sets the ground for a possible self-assembling of 3D superstructures with extended stability ranges. Here we first describe the trapping mechanism on the case of a single discilination line and then use the results to demonstrate the trapping in the blue phase II. Effects of particle sizes ranging from submicron to 50 nanometers are examined. The assembling in blue phases is expected to form photonic crystals that can be easily manipulated via affecting the liquid crystal matrix and/or colloidal particles. © 2010 SPIE.

Abstract:

In patchy particle systems where there is competition between the self-assembly of finite clusters and liquid-vapour phase separation, reentrant phase behaviour is observed, with the system passing from a monomeric vapour phase to a region of liquid-vapour phase coexistence and then to a vapour phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of reentrance. However, for the most physically reasonable parameter values of the model, this behaviour is restricted to a certain range of density, with phase separation still persisting at high densities.