Entanglement Entropy and Entanglement Spectrum of the Kitaev Model

2010/01/31 by Hong Yao, Xiao-Liang Qi · 14 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Entropy (arrow of time) #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Spectrum (functional analysis) #Squashed entanglement #Statistical physics #Theoretical physics #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevlett.105.080501

published as Phys. Rev. Lett., 105, 080501 (2010) · 4.0 pages + supplementary material, published version in Phys. Rev. Lett

openalex publication_date 2010/08/16 · arxiv created 2010/08/18 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this letter, we obtain an exact formula for the entanglement entropy of the ground state and all excited states of the Kitaev model. Remarkably, the entanglement entropy can be expressed in a simple separable form S = SG+SF, with SF the entanglement entropy of a free Majorana fermion system and SG that of a Z2 gauge field. The Z2 gauge field part contributes to the universal "topological entanglement entropy" of the ground state while the fermion part is responsible for the nonlocal entanglement carried by the Z2 vortices (visons) in the non-Abelian phase. Our result also enables the calculation of the entire entanglement spectrum and the more general Renyi entropy of the Kitaev model. Based on our results we propose a new quantity to characterize topologically ordered states--the capacity of entanglement, which can distinguish the st ates with and without topologically protected gapless entanglement spectrum.

Citations

• Calculation of reduced density matrices from correlation functions
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Non-Abelian anyons and topological quantum computation

Cited by

• Entanglement spectrum: Identification of the transition from vortex-liquid to vortex-lattice state in a weakly interacting rotating Bose-Einstein condensate
• Exact Organization of Density Matrices and Entanglement Structure in the Kitaev Spin Liquid
• Entanglement and Majorana edge states in the Kitaev model
• Position-momentum duality in the entanglement spectrum of free fermions
• Edge-mode combinations in the entanglement spectra of non-Abelian fractional quantum Hall states on the torus
• Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Topological and entanglement properties of resonating valence bond wave functions
• Phase diagram of quantum critical system via local convertibility of ground state
• Tensor network implementation of bulk entanglement spectrum
• Entanglement dualities in supersymmetry
• Diagnosing Topological Edge States via Entanglement Monogamy
• Exact chiral spin liquid with stable spin Fermi surface on the kagome lattice
• Microscopic models for Kitaev's sixteenfold way of anyon theories

Related

• Entanglement and Majorana edge states in the Kitaev model
• Ground state entanglement and geometric entropy in the Kitaev model
• Anatomy of Fermionic Entanglement and Criticality in Kitaev Spin Liquids
• ENTANGLEMENT ENTROPY AND STRONGLY CORRELATED TOPOLOGICAL MATTER
• Exact Organization of Density Matrices and Entanglement Structure in the Kitaev Spin Liquid