Gauge field entanglement in Kitaev's honeycomb model

B. Dóra, Roderich Moessner

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 a minimal entropy ground-state wave function 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 -ln2 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 (Ny-1)ln2, with Ny 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.

Original languageEnglish
Article number035109
JournalPhysical Review B
Volume97
Issue number3
DOIs
Publication statusPublished - Jan 5 2018

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Gages
Entropy
entropy
Hamiltonians
Fermions
partitions
sectors
fermions
Jordan
circumferences
Wave functions
tracing
Ground state
degrees of freedom
wave functions
ground state
Liquids
symmetry
liquids

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Gauge field entanglement in Kitaev's honeycomb model. / Dóra, B.; Moessner, Roderich.

In: Physical Review B, Vol. 97, No. 3, 035109, 05.01.2018.

Research output: Contribution to journalArticle

Dóra, B. ; Moessner, Roderich. / Gauge field entanglement in Kitaev's honeycomb model. In: Physical Review B. 2018 ; Vol. 97, No. 3.
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