Topological order from quantum loops and nets

Journal Article · Mon Dec 15 04:00:00 EST 2008 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.04.011· OSTI ID:21167691

Fendley, Paul ^[1]

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1. All Souls College and the Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, OX1 3NP (United Kingdom)

I define models of quantum loops and nets that 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 simple Hamiltonian preserving the topological order is found by exploiting quantum self-duality. For the square lattice, this Hamiltonian has only four-spin interactions.

• OSTI ID: 21167691
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 323; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANYONS
DUALITY
EXCITED STATES
GROUND STATES
HAMILTONIANS
POLYNOMIALS
QUANTUM MECHANICS
SPIN
TETRAGONAL LATTICES
TOPOLOGY