Electric circuit emulation of topological transitions driven by quantum statistics

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.

6 pages, 3 figures + Supplementary 11 pages, 3 figures

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Repulsively bound atom pairs in an optical lattice
• Fractional statistics in anyon collisions
• Topological properties of linear circuit lattices
• Fractional Quantum Hall State in Coupled Cavities
• Gain and loss induced topological insulating phase in a non Hermitian electrical circuit
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Two-body physics in the Su-Schrieffer-Heeger model
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Topological two-body bound states in the interacting Haldane model

Cited by in corpus (5)

• Observation of type-III corner states induced by long-range interactions
• Engineering topological states and quantum-inspired information processing using classical circuits
• Effects of Peierls phases in open linear chains
• Emergence of anyonic correlations from spin and charge dynamics in one dimension
• Topological edge states in all-dielectric square-lattice arrays of bianisotropic microwave resonators