This series consists of talks in the area of Condensed Matter.
We consider one dimensional devices supporting a pair of Majorana bound states at their ends We firstly show  that edge Majorana bound modes allow for processes with an actual transfer of electronic material between well-separated points and provide an explicit computation of the tunnelling amplitude for this process.
The simulation of systems of anyons offers a significant challenge to
the condensed matter physicist. These systems are presently of
substantial theoretical and experimental interest due to their potential
for universal quantum computation, but due to their non-trivial exchange
statistics, the tools available for their study have been limited. In
this talk, I will present a formalism whereby any existing tensor
network algorithm may be adapted for use with both Abelian and
non-Abelian anyons, culminating in our recent simulations of infinite
Anderson localization emerges in quantum systems when randomised parameters cause the exponential suppression of motion. In this talk we will consider the localization phenomenon in the toric code, demonstrating its ability to sustain quantum information in a fault tolerant way. We show that an external magnetic field induces quantum walks of anyons, causing logical information to be destroyed in a time linear with the system size when even a single pair of anyons is present.
More than forty years ago Nobel laureate P.W. Anderson studied the overlap between two nearby ground states. The result that the overlap tends to zero in the thermodynamics limit was catastrophic for those times. More recently the study of the overlap between ground states, i.e. the fidelity, led to the formulation of the so called fidelity approach to (quantum) phase transition (QPT).
AdS/CFT has proven itself a powerful tool in extending our understanding of strongly coupled quantum theories. While studies of AdS/CFT have predominantly focused on tree level calculations, there has been growing interest in the loop effect recently. We studied the 1-loop correction to the gauge boundary-to-boundary correlator due to its coupling to a complex scalar field. In this talk, I would outline our main results, explain the Cutkosky rule in AdS space, and discuss an extra divergence we found in both real and imaginary part of the loop integral.
Entanglement renormalization is a coarse-graining transformation for quantum lattice systems. It produces the multi-scale entanglement renormalization ansatz, a tensor network state used to represent ground states of strongly correlated systems in one and two spatial dimensions. In 1D, the MERA is known to reproduce the logarithmic violation of the boundary law for entanglement entropy, S(L)~log L, characteristic of critical ground states. In contrast, in 2D the MERA strictly obeys the entropic boundary law, S(L)~L, characteristic of gapped systems and a class of critical systems.
In this talk I will describe my recent work on the structure of entanglement in field theory from the point of view of mutual information. I will give some basic scaling intuition for the entanglement entropy and then describe how this intuition is better captured by the mutual information. I will also describe a proposal for twist operators that can be used to calculate the mutual information using the replica method. Finally, I will discuss the relevance of my results for holographic duality and entanglement based simulation methods for many body systems.