Family of non-Abelian Kitaev models on a lattice: Topological condensation and confinement

2007/12/31 by Héctor Bombín, H. Bombin, M. A. Martín-Delgado +1 · 5 citations
Mathematics · Physics and Astronomy · #Abelian group #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Discrete symmetry #Gauge theory #Geometry #Homogeneous space #Lattice (music) #Mathematics #Physics #Pure mathematics #Quantum many-body systems #Quantum mechanics #Symmetry protected topological order #Theoretical physics #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.str-el #hep-th #quant-ph

paper · pdf · doi:10.1103/physrevb.78.115421

published as Phys.Rev.B78:115421,2008 · Additinal figures, minor corrections

openalex publication_date 2008/09/22 · arxiv created 2008/09/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction in the discrete gauge symmetry with respect to the original systems, which corresponds to a generalized mechanism of explicit symmetry breaking. The topological order is either partially lost or completely destroyed throughout the various models. The systems display condensation and confinement of the topological charges present in the standard non-Abelian Kitaev models, which we study in terms of ribbon operator algebras.

Citations

• Linear Representations of Finite Groups
• Discrete non-Abelian gauge theories in Josephson-junction arrays and quantum computation
• 2D multipartite valence bond states in quantum anti-ferromagnets
• TOPOLOGICAL ORDERS IN RIGID STATES
• Information and computation: Classical and quantum aspects
• Homological error correction: Classical and quantum codes
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Topologically protected quantum bits using Josephson junction arrays
• Equivalence of the resonating-valence-bond and fractional quantum Hall states
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Implementation of Spin Hamiltonians in Optical Lattices
• Large-Nexpansion for frustrated quantum antiferromagnets
• Ground-state degeneracy of the fractional quantum Hall states in the presence of a random potential and on high-genus Riemann surfaces
• Ground States of Quantum Antiferromagnets in Two Dimensions
• THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS
• Mean-field theory of spin-liquid states with finite energy gap and topological orders
• String-net condensation: A physical mechanism for topological phases
• Topological quantum memory
• Topological Computation without Braiding
• Fault-tolerant quantum computation by anyons
• Chiral spin states and superconductivity
• A Modular Functor Which is Universal¶for Quantum Computation
• Topological quantum computation
• Fractionalization in the Cuprates: Detecting the Topological Order
• Quantum orders and symmetric spin liquids

Cited by

• Gapped Boundaries of Kitaev's Quantum Double Models: A Lattice Realization of Anyon Condensation from Lagrangian Algebras
• Reconstructing non-Abelian braiding and fusion without anyon transport
• Scaling law for topologically ordered systems at finite temperature
• Universal gates from braiding and fusing anyons on quantum hardware
• Fusion basis for lattice gauge theory and loop quantum gravity

Related

• A non-semisimple Kitaev lattice model
• Classical analogue to the Kitaev model and Majorana-like topological bound states
• Discrete quantum systems from topological field theory
• Emergence of new topological gapless phases in the modified square-lattice Kitaev model
• Topological lattice field theories from intertwiner dynamics