Talks

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this talk, we study the entanglement entropy of 2D topological phases from the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system encodes the quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the entanglement boundary. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries. 

 In the framework of ontological models, the features of quantum

theory that emerge as inherently nonclassical always involve properties that

are fine tuned, i.e.  properties that hold at the operational level but break at the

ontological level (they only hold for fine tuned values of the ontic parameters). Famous

examples of fine tuned properties are noncontextuality and locality. We here

develop a precise theory-independent mathematical framework for characterizing

operational fine tunings. These are distinct from causal fine tunings — already

introduced by Wood and Spekkens — as they do not involve any assumption

on the underlying causal structure. We show how all the already known examples of

operational fine tunings fit into our framework, we discuss possibly new fine tunings

and we use the framework to shed new light on the relation between nonlocality

and generalized contextuality. The framework is set in the language of functors in category

theory and it aims at unifying the spooky properties of quantum theory as well as

accounting for new ones.

Magnetic skyrmions are topological solitons which occur in a large class of ferromagnetic materials and which  are currently attracting much attention, not least because of their potential use for  low-energy magnetic information storage and manipulation. The talk is about an integrable model for magnetic skyrmions, introduced in a recent paper (arxiv:1812.07268) and generalised in  arxiv:1905.06285. The model is based on a geometrical interpretation of the Dzyaloshinskii-Moriya interaction in terms of a non-abelian gauge field.  In the talk will explain the model and the geometry behind its solution, and discuss solutions and their applications.