The Composite Particle Duality: A New Class of Topological Quantum Matter

The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or as a dynamical physical mechanism. The immediate implication of the duality is that an interacting quantum system in arbitrary dimensions can experience a modification of its statistical properties if coupled to a certain gauge field. In other words, commutation relations of quantum fields can be effectively modified by a dynamical physical process. For instance, an originally bosonic quantum fluid in $d$ spatial dimensions can feature composite fermionic (or anyonic) excitations when coupled to a statistical gauge field. In 3+1D the mechanism of flux attachment induces a dynamical formation of dyons as higher-dimensional analogues of Laughlin quasiparticles. In 1+1D there is lack of flux attachment but a remnant in the form of a statistical gauge field can be explicitly constructed. We also introduce a family of interacting quantum many-body systems that undergo statistical transmutation as indicated by the duality. This opens the door to a new realm of topological phases across dimensions both in lattice and continuum systems.