Low-energy physics of a superfluid vortex lattice

Superfluidity is one of the most intriguing quantum phenomena that emerges at temperatures close to absolute zero. Vortices with quantized circulation are the hallmark of superfluidity and are created under external rotation. If the number of vortices is much smaller than the number of particles, vortices arrange themselves in a triangular lattice that exhibits intriguing collective dynamics. Quantum vortex crystals in superfluids and superconductors have been one of the exciting avenues of research for many decades. In this talk I will introduce an effective field theory built from low-energy degrees of freedom which captures universal properties of vortex lattices in bosonic superfluids. I will present our results for current and stress tensor Hall responses and will provide some arguments that the Hall viscosity of a quantum vortex crystal vanishes at zero frequency and momentum. In the end of the talk, I will describe new directions that we are currently exploring using this effective field theory.