On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity

TL;DR

This paper develops a duality framework to understand quantum melting of vortex crystals in superfluids, introducing a gravity analogy and analyzing defect-driven melting scenarios within a Lifshitz model.

Contribution

It introduces a fracton-elasticity duality for vortex lattices and proposes a dual gravity description, advancing understanding of quantum melting in superfluid vortex crystals.

Findings

Developed a duality framework linking vortex lattice physics to emergent gravity.

Analyzed quantum melting scenarios via topological defect proliferation.

Layed groundwork for a gravity-based description of superfluid vortex matter.

Abstract

Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals.