Entanglement of a 3D generalization of the Kitaev model on the diamond lattice

Abstract

We study the entanglement properties of a three dimensional generalization of the Kitaev honeycomb model proposed by Ryu [Phys. Rev. B 79, 075124, (2009)]. The entanglement entropy in this model separates into a contribution from a $Z_2$ gauge field and that of a system of hopping Majorana fermions, similar to what occurs in the Kitaev model. This separation enables the systematic study of the entanglement of this 3D interacting bosonic model by using the tools of non-interacting fermions. In this way, we find that the topological entanglement entropy comes exclusively from the $Z_2$ gauge field, and that it is the same for all of the phases of the system. There are differences, however, in the entanglement spectrum of the Majorana fermions that distinguish between the topologically distinct phases of the model. We further point out that the effect of introducing vortex lines in the $Z_2$ gauge field will only change the entanglement contribution of the Majorana fermions. We evaluate this contribution to the entanglement which arises due to gapless Majorana modes that are trapped by the vortex lines.

arXiv comment25 pages, 5 figures. Invited article to JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physics

References in corpus (34)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement in quantum critical phenomena
• Topological entanglement entropy
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Entanglement spectrum of a topological phase in one dimension
• Calculation of reduced density matrices from correlation functions
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Reduced density matrices and entanglement entropy in free lattice models
• Inversion Symmetric Topological Insulators
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Entanglement spectrum of topological insulators and superconductors
• The Flux-Phase of the Half-Filled Band
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• The entanglement gap and a new principle of adiabatic continuity
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains
• Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
• Universal entanglement entropy in 2D conformal quantum critical points
• Topological Entanglement and Clustering of Jain Hierarchy States
• Statistical Topological Insulators
• A $\Gamma$-matrix generalization of the Kitaev model
• Three-dimensional topological phase on the diamond lattice
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Pressure-induced transition from the dynamic to static Jahn-Teller effect in (Ph${}_4$P)${}_2$IC${}_{60}$

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• Entanglement in 3D Kitaev Spin Liquids
• Entanglement of Free Fermions and Bosons at Finite Temperature