Gauge field entanglement of Kitaev's honeycomb model

Abstract

A spin fractionalizes into matter and gauge fermions in Kitaev's spin liquid on the honeycomb lattice. This follows from a Jordan-Wigner mapping to fermions, allowing for the construction of minimal entropy ground state wavefunction on the cylinder. We use this to calculate the entanglement entropy by choosing several distinct partitionings. First, by partitioning an infinite cylinder into two, the $-\ln 2$ topological entanglement entropy is reconfirmed. Second, the reduced density matrix of the gauge sector on the full cylinder is obtained after tracing out the matter degrees of freedom. This allows for evaluating the gauge entanglement Hamiltonian, which contains infinitely long range correlations along the symmetry axis of the cylinder. The matter-gauge entanglement entropy is $(N_y-1)\ln 2$ with $N_y$ the circumference of the cylinder. Third, the rules for calculating the gauge sector entanglement of any partition are determined. Rather small correctly chosen gauge partitions can still account for the topological entanglement entropy in spite of long-range correlations in the gauge entanglement Hamiltonian.

arXiv comment7 pages, 5 figures

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Cited by in corpus (6)

• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
• Confinement transition in a Kitaev-like honeycomb model with bond anisotropy
• Majorana Fermion Mean-Field Theories of Kitaev Quantum Spin Liquids
• Quenching the Kitaev honeycomb model
• Unveiling topological order through multipartite entanglement