Electric circuit emulation of topological transitions driven by quantum statistics

TL;DR

This paper predicts a topological transition in a two-particle system driven by quantum statistics, and proposes emulating these states using resonant electric circuits, bridging quantum physics and circuit technology.

Contribution

It introduces a novel topological transition driven by quantum statistics in an interacting system and develops a method to emulate these states with electric circuits.

Findings

Topological edge states depend on particle quantum statistics.

Electric circuit emulation accurately reproduces anyon pair eigenmodes.

Quantum statistics can control topological phase transitions.

Abstract

Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are typically controlled by the external parameters. In contrast, in this Letter, we predict the topological transition in the two-particle interacting system driven by the particles' quantum statistics. As a toy model, we investigate an extended one-dimensional Hubbard model with two anyonic excitations obeying fractional quantum statistics in-between bosons and fermions. 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 electric circuits.