Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical Physics Supplement

A Short Introduction to Fibonacci Anyon Models(Interaction and Nanostructural Effects in Low-Dimensional Systems)

Simon Trebst, Matthias Troyer, Zhenghan Wang, Andreas Ludwig

Published Feb 5, 2009• 0 citations
OpenAlex

Related papers

Dynamical Vertex Approximation : An Introduction(Interaction and Nanostructural Effects in Low-Dimensional Systems)

Karsten Held, A. A. Katanin, A. Toschi

Progress of Theoretical Physics Supplement•Feb 5, 2009•0 citations

From Multiple Integrals to Fredholm Determinants(Interaction and Nanostructural Effects in Low-Dimensional Systems)

Alexander Seel, Frank Göhmann, Andreas Klümper

Progress of Theoretical Physics Supplement•Feb 5, 2009•0 citations

Interacting anyons in one dimension: The Fibonacci chain

Andreas W. W. Ludwig, Adrian E. Feiguin, Simon Trebst +4 more

Bulletin of the American Physical Society•Mar 6, 2007•0 citations

A Short Introduction to Fibonacci Anyon Models

Simon Trebst, Matthias Troyer, Zhenghan Wang +1 more

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial (“identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the “golden chain”, a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian SU(2)k statistics. The k→∞ limit of the latter yields ordinary SU(2) spin chains.

arXiv:0902.3275•Progress of Theoretical Physics Supplement•Jan 1, 2008•167 citations

Phases of interacting Fibonacci anyons on a ladder at half-filling

Nico Kirchner, Roderich Moessner, Frank Pollmann +1 more

Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles, it is natural to ask what phases can arise in interacting many-anyon systems. To study this topic, we consider the particular case of Fibonacci anyons subject to an anyonic tight-binding model with nearest-neighbor repulsion on a two-leg ladder. Focusing on the case of half-filling, for low interaction strengths an “anyonic” metal is found, whereas for strong repulsion, the anyons form an insulating charge-density wave. Within the latter regime, we introduce an effective one-dimensional model up to sixth order in perturbation theory arising from anyonic superexchange processes. We numerically identify four distinct phases of the effective model, which we characterize using matrix product state methods. These include both the ferro- and antiferromagnetic golden chain phases, as well as phases with Z 2 and incommensurate correlations.

arXiv:2507.22115•Physical review. B./Physical review. B•Jun 23, 2026•0 citations

A simple quasi-1D model of Fibonacci anyons

David Aasen, Roger S. K. Mong, David J. Clarke +2 more

Bulletin of the American Physical Society•Mar 2, 2015•0 citations
We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial (“identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the “golden chain”, a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian SU(2)k statistics. The k→∞ limit of the latter yields ordinary SU(2) spin chains.
Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles, it is natural to ask what phases can arise in interacting many-anyon systems. To study this topic, we consider the particular case of Fibonacci anyons subject to an anyonic tight-binding model with nearest-neighbor repulsion on a two-leg ladder. Focusing on the case of half-filling, for low interaction strengths an “anyonic” metal is found, whereas for strong repulsion, the anyons form an insulating charge-density wave. Within the latter regime, we introduce an effective one-dimensional model up to sixth order in perturbation theory arising from anyonic superexchange processes. We numerically identify four distinct phases of the effective model, which we characterize using matrix product state methods. These include both the ferro- and antiferromagnetic golden chain phases, as well as phases with Z 2 and incommensurate correlations.