Lattice Model for Fermionic Toric Code

Abstract

The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact soluble string-net models. However, the most important topologically ordered phases of matter are arguably the fermionic fractional quantum Hall states. Topological phases of matter for fermion systems are strictly richer than their bosonic counterparts because locality has different meanings for the two kinds of systems. In this paper, we describe a simple fermionic version of the toric code model to illustrate many salient features of fermionic exactly soluble models and fermionic topologically ordered states.

10 pages, 12 figures, published version

References in corpus (6)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Topological boundary conditions in abelian Chern-Simons theory
• Mutual Chern-Simons theory for Z_2 topological order

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