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

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.

19 pages, 1 figure. v2: published version

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Cited by in corpus (8)

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
• Quadrupole gauge theory: anti-Higgs mechanism and elastic dual
• Topological Dipole Insulator
• Non-equilibrium charge-vortex duality
• Non-commutative effective field theory of the lowest Landau level superfluid
• Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation
• Effective field theory for the superfluid vortex lattice from coset construction