Extended Hubbard Model with Ring Exchange: A Route to a Non-Abelian Topological Phase

2003/12/31 by Michael Freedman, Chetan Nayak, Kirill Shtengel · 6 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Physics of Superconductivity and Magnetism #Topological Materials and Phenomena #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.94.066401

published as Phys. Rev. Lett. 94, 066401 (2005) · 4 pages, 2 colour figures, submitted to PRL. For an extended treatment of a more general family of models see cond-mat/0309120

arxiv created 2004/11/09 · openalex publication_date 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an extended Hubbard model on a 2D kagome lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling fraction 1/6, where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the "d-isotopy" transition point into a stable phase with a certain type of non-Abelian topological order. Near the "special" values, d=2cos(pi/(k+2), this topological phase has anyonic excitations closely related to SU(2) Chern-Simons theory at level k.

Citations

• Topologically protected quantum bits using Josephson junction arrays
• Equivalence of the resonating-valence-bond and fractional quantum Hall states
• Fault-tolerant quantum computation by anyons
• Nonabelions in the fractional quantum hall effect

Cited by

• Homological error correction: Classical and quantum codes
• Anyonic interferometry and protected memories in atomic spin lattices
• Operator quantum error-correcting subsystems for self-correcting quantum memories
• Spectrum of the non-abelian phase in Kitaev’s honeycomb lattice model
• Anyonic braiding in optical lattices
• Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids

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