Quantum vortex lattice: Lifshitz duality, topological defects and multipole symmetries

TL;DR

This paper develops a dual gauge theory framework for a vortex lattice in a 2D superfluid, revealing topological defects, multipole symmetries, and a quantum melting transition to a vortex supersolid.

Contribution

It introduces a novel dual gauge theory formulation of vortex lattices, incorporating Lifshitz theory, multipole symmetries, and topological defect classification.

Findings

Dual gauge theory describes vortex lattice dynamics.

Identifies multipole symmetries and their role in defect mobility.

Proposes a mean-field theory for vortex crystal to supersolid transition.

Abstract

We study an effective field theory of a vortex lattice in a two-dimensional neutral rotating superfluid. Utilizing particle-vortex dualities, we explore its formulation in terms of a $U(1)$ gauge theory coupled to elasticity, that at low energies reduces to a compact Lifshitz theory augmented with a Berry phase term encoding the vortex dynamics in the presence of a superflow. Utilizing elasticity- and Lifshitz-gauge theory dualities, we derive dual formulations of the vortex lattice in terms of a traceless symmetric scalar-charge theory and demonstrate low-energy equivalence of our dual gauge theory to its elasticity-gauge theory dual. We further discuss a multipole symmetry of the vortex lattice and its dual gauge theory's multipole one-form symmetries. We also study its topological crystalline defects, where the multipole one-form symmetry plays a prominent role. It classifies the defects, explains their restricted mobility, and characterizes descendant vortex phases, which includes a novel vortex supersolid phase. Using the dual gauge theory, we also develop a mean-field theory for the quantum melting transition from a vortex crystal to a vortex supersolid.