Interacting non-Abelian anyons in an exactly solvable lattice model

In this thesis, we study the non-Abelian anyons that emerge as vortices in Ki-taev's honeycomb spin lattice model. By generalizing the solution of the model, we explicity demonstrate the non-Abelian fusion rules and the braid statistics that charaterize the anyons. This is based on showing the presence of vortices leads to zero modes in the spectrum. These can acquire finite energy due to short range vortex-vortex interactions. By studying the spectral evolution as a function of the vortex seperation, we unambigously identify the zero modes with the fusion degrees of freedom of non-Abelian anyons. To calculate the non-Abelian statistics, we show how the vortex transport can be implemented through local manipulation of the couplings. This enables us to employ the eigenstates of the model to simulate a process where a vortex winds around another. The corresponding evolution of the degenerate ground state space is given by a Berry phase, which under suitable conditions coincides with the statistics. By considering a range of finite size systems, we find a physical regime where the Berry phase gives the predicted statistics of the anoyonic vortices with high fidelity. Finally we study the full-vortex sector of the model and find that is supports a previously undiscovered topological phase. This new phase emerges from the phase with non-Abelian anyons due to their interactions. To study the transitions between the different topological phases appearing in the model, we consider Fermi surface, whose topology captures the long-range properties. Each phase is found to be characterized by a distinct number of Fermi points, with the number depending on distinct global Hamiltonian symmetries. To study how the Fermi surfaces evolve into each other at phase transitions, we consider the low-energy field theory that is described by Dirac fermions. We show that phase transition driving perturbations translate to a coupling to chiral gauge fields, that always lead to Fermi point transport. By studying this transport, we obtain analytically the extended phase space of the model and its properties

Diagnosing Topological Edge States via Entanglement Monogamy

Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix. This matrix is often tractable either analytically or numerically, and it precisely captures the relevant correlations of the system. By invoking the concept of monogamy of entanglement, we show that highly entangled states supported across a system bipartition are largely disentangled from the rest of the system, thus, usually appearing as gapless edge states. We then define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. We demonstrate the versatility of this qualifier by applying it to various free and interacting fermionic topological systems

Janus-dendrimer supramolecular structures as delivery agents for small molecules, peptides and proteins

Janus-dendrimers are synthetic amphiphiles formed by linking two chemically distinct hydrophilic and hydrophobic dendrons by their core, which can self-assemble as vesicles (dendrimersomes) or fibres in aqueous solutions, as well as in biological media. This research shows that the dendrimersome scan differentially encapsulate drug compounds, are stable for long periods of time, and can be annealed from 22 °C to 70 °C with minimal change (2-5 nm)in their hydrodynamic radius [1].Also, by modulating the hydrophilic branch generation we found that Janus-dendrimers were also able to self-assemble into a variety of other architectures such as fibres, giving rise to supramolecular hydrogels capable of encapsulating and releasing small molecules, peptides, and proteins[2],or even function as colloidal suspensions’ stabilizers [3].Thus, the small library of Janus-dendrimers reported herein expand the scope of dendrimer-based supramolecular drug delivery systems and suggest that these materials can be further used in biomedical sol–gel applications