2008/01/01 by Simon Trebst, Matthias Troyer, Zhenghan Wang +1 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anyon #Combinatorics #Fibonacci number #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum many-body systems #Quantum mechanics #Spin (aerodynamics) #Theoretical physics #Topological quantum computer #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1143/ptps.176.384
published as Prog. Theor. Phys. Supp. 176, 384 (2008)
openalex publication_date 2008/01/01 · arxiv created 2009/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.