### 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 language | English |
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Article number | 035109 |

Journal | Physical Review B |

Volume | 97 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 5 2018 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

*Physical Review B*,

*97*(3), [035109]. https://doi.org/10.1103/PhysRevB.97.035109

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

Research output: Contribution to journal › Article

*Physical Review B*, vol. 97, no. 3, 035109. https://doi.org/10.1103/PhysRevB.97.035109

}

TY - JOUR

T1 - Gauge field entanglement in Kitaev's honeycomb model

AU - Dóra, B.

AU - Moessner, Roderich

PY - 2018/1/5

Y1 - 2018/1/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85040324491&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040324491&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.97.035109

DO - 10.1103/PhysRevB.97.035109

M3 - Article

AN - SCOPUS:85040324491

VL - 97

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 3

M1 - 035109

ER -