Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids

Abstract

We analyse in detail the effect of non-trivial band topology on the area law behaviour of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model into 1D fermionic subsystems, we identify those subsystems responsible for universal entanglement contributions in the gapped phases and those responsible for critical entanglement scaling in the gapless phases. For the gapped phases we analytically show how the topological edge states contribute to the entanglement entropy and provide a universal lower bound for it. For the gapless semi-metallic phases and topological phase transitions the identification of the critical subsystems shows that they fall always into the Ising or the XY universality classes. As our study concerns the fermionic degrees of freedom in the honeycomb model, qualitatively similar results are expected to apply also to generic topological insulators and superconductors.

12+6 pages, 11+5 figures

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Cited by in corpus (9)

• Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field
• Topological Quantum Liquids with Long-Range Couplings
• Disorder in the Sachdev-Yee-Kitaev Model
• Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Phase space methods for Majorana fermions
• Gauge field entanglement of Kitaev's honeycomb model
• Abelian and non-Abelian chiral spin liquids in a compact tensor network representation
• Conformal energy currents on the edge of a topological superconductor