Sergej Moroz (Karlstad University) gives a webinar on ‘Superfluid vortex crystals and their quantum melting’.

I will present our investigations of a low-energy effective field theory of a two-dimensional superfluid vortex crystal which reduces to a scalar Lifshitz theory in the linearized approximation. General symmetry considerations allow us to determine non-linear terms that fix a decay rate of a unique collective gapless Tkachenko mode which disperses quadratically at low momenta. I will also introduce a linearized fracton-elasticity duality adapted to the vortex crystal that allows to incorporate naturally topological crystalline defects such as disclinations and dislocations. Based on that duality, I will discuss possible scenarios of melting of the vortex crystal due to quantum fluctuations. Finally, I will present our first steps towards a non-linear extension of the elasticity duality which gives rise to a dynamical theory of gravity.