Chiral vortex-line liquid of three-dimensional interacting Bose systems with moat dispersion

We formulate and investigate a quantum state, the chiral vortex-line liquid (CVLL), emerging in three-dimensional interacting Bose systems exhibiting moat-band dispersions. Such dispersions feature extensive degeneracy along closed manifolds in momentum space, significantly amplifying quantum fluctuations that suppress conventional Bose-Einstein condensation. By extending the two-dimensional Chern-Simons (CS) flux-attachment transformation to three dimensions through a combination of planar CS phases and Jordan-Wigner fermionization along vortex lines, we construct the CVLL state, characterized by preserved rotational <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>S</a:mi><a:mi>O</a:mi><a:mo>(</a:mo><a:mn>2</a:mn><a:mo>)</a:mo></a:mrow></a:math> symmetry, broken time-reversal symmetry, nontrivial vortex-line excitations, and topological gapless edge surface states. We construct the associated field theory in a curved spatial geometry and analyze the low-energy effective theory of the CVLL state, demonstrating its topological nature. Using Monte Carlo simulations, we numerically determine the scaling of the chemical potential of the CVLL ground state as a function of boson density for interacting bosons in a cylindrical moat-band geometry and demonstrate that the CVLL phase energetically outcompetes traditional condensate phases at low densities, highlighting its relevance to experimental platforms including frustrated quantum magnets, ultracold atomic gases, excitonic systems, the physics of rotons in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>He</b:mi><b:mprescripts/><b:none/><b:mn>4</b:mn></b:mmultiscripts></b:math>, and moat regimes in heavy-ion collisions.