Numerical simulation of non-Abelian anyons

Kirchner, Nico; Millar, Darragh; Ayeni, Babatunde M.; Smith, Adam; Slingerland, Joost K.; Pollmann, Frank

Abstract

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general Abelian and non-Abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons, and Ising anyons. Additionally, we simulate nonequilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times - indicating thermalization.

Citation

Kirchner, N., Millar, D., Ayeni, B. M., Smith, A., Slingerland, J. K., & Pollmann, F. (2023). Numerical simulation of non-Abelian anyons. Physical Review B, 107(19), Article 195129. https://doi.org/10.1103/physrevb.107.195129

• Journal Article Type: Article
• Acceptance Date: Apr 7, 2023
• Online Publication Date: May 15, 2023
• Publication Date: May 15, 2023
• Deposit Date: Jun 22, 2023
• Publicly Available Date: Jun 27, 2023
• Journal: Physical Review B
• Print ISSN: 2469-9950
• Electronic ISSN: 2469-9969
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 107
• Issue: 19
• Article Number: 195129
• DOI: https://doi.org/10.1103/physrevb.107.195129
• Public URL: https://nottingham-repository.worktribe.com/output/20841511
• Publisher URL: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.195129