Topological transitions driven by quantum statistics and their electrical circuit emulation

Topological phases exhibit a plethora of striking phenomena, including disorder-robust localization and the propagation of waves of various nature. While this physics is actively explored in bosonic and fermionic cases, the topological phases of anyons ??? particles with fractional quantum statistics ??? are largely uncharted. Here, we unveil the topological transition mediated by the particles??? quantum statistics that arises for two-anyon and threeanyon excitations in a one-dimensional array described by the extended Hubbard model. As we demonstrate, the interplay of two-particle interactions and tunneling processes enables topological edge states of anyon pairs whose existence and localization at one or another edge of the one-dimensional system is governed by the quantum statistics of particles. Since a direct realization of the proposed system is challenging, we develop a rigorous method to emulate the eigenmodes and eigenenergies of anyon pairs with resonant electrical circuits.

Automated summary

Topological transition mediated by quantum statistics is discovered for two-anyon and three-anyon excitations in a one-dimensional array, showing the existence of topological edge states governed by the quantum statistics of particles.