vix.ing · top · new · best · stats · spec

Topological order from quantum loops and nets

2008/04/15 by Paul Fendley · 2 citations
Computer Science · Physics and Astronomy · #Combinatorics #Hamiltonian (control theory) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological degeneracy #Topological entropy in physics #Topological order #Topological quantum computer #Topological quantum number #Topology (electrical circuits) #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1016/j.aop.2008.04.011

published as Annals of Physics 323 (2008) 3113

arxiv created 2008/04/15 · openalex publication_date 2008/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

I define models of quantum loops and nets which have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With the appropriate inner product, these quantum loop models are equivalent to net models whose topological weight involves the chromatic polynomial. A useful consequence is that the models have a quantum self-duality, making it possible to find a simple Hamiltonian preserving the topological order. For the square lattice, this Hamiltonian has only four-spin interactions.

Citations

Cited by