Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids

2008/10/31 by Charlotte Gils, Eddy Ardonne, Simon Trebst +3 · 11 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.mes-hall #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.103.070401

published as Phys. Rev. Lett. 103, 070401 (2009). · 4 pages, 2 figures

arxiv created 2009/06/19 · openalex publication_date 2009/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum mechanical systems, whose degrees of freedom are so-called su(2)k anyons, form a bridge between ordinary SU(2) quantum magnets (of arbitrary spin-S) and systems of interacting non-Abelian anyons. Anyonic spin-1/2 chains exhibit a topological protection mechanism that stabilizes their gapless ground states and which vanishes only in the limit (k-->infinity) of the ordinary spin-1/2 Heisenberg chain. For anyonic spin-1 chains the phase diagram closely mirrors the one of the biquadratic SU(2) spin-1 chain. Our results describe, at the same time, nucleation of different 2D topological quantum fluids within a "parent" non-Abelian quantum Hall state, arising from a macroscopic occupation with localized, interacting anyons. The edge states between the "nucleated" and the parent liquids are neutral, and correspond precisely to the gapless modes of the anyonic chains.

Citations

• Non-Abelian anyons and topological quantum computation
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• From Luttinger liquid to non-Abelian quantum Hall states
• Entanglement in valence-bond-solid states on symmetric graphs
• A Short Introduction to Fibonacci Anyon Models
• Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
• Condensate-induced transitions and critical spin chains
• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Russian doll spectrum in a non-Abelian string-net ladder
• Kitaev model and dimer coverings on the honeycomb lattice
• Non-Abelian Anyons: When Ising Meets Fibonacci
• Exact solution of theD3non-Abelian anyon chain
• Critical-entanglement spectrum of one-dimensional symmetry-protected topological phases

Related

• Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids
• Landscapes of an out-of-equilibrium anyonic sea
• Chiral Edge States Emerging on Anyon-Net
• Anyon condensation, topological quantum information scrambling, and Andreev-like reflection of non-Abelian anyons in quantum Hall interfaces
• Landau-Ginzburg Paradigm of Topological Phases