Gauge field entanglement of Kitaev's honeycomb model

TL;DR

This paper investigates the entanglement properties of gauge and matter sectors in Kitaev's honeycomb model, confirming topological entanglement entropy and analyzing gauge entanglement structure using a fermionic mapping.

Contribution

It provides a detailed analysis of gauge and matter entanglement in Kitaev's honeycomb model, including methods to compute gauge entanglement and the impact of partitioning choices.

Findings

Reconfirmed the topological entanglement entropy as -ln 2.

Derived the gauge entanglement Hamiltonian with long-range correlations.

Established rules for calculating gauge sector entanglement in various partitions.

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 minimal entropy ground state wavefunction 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 $-\ln 2$ 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 $(N_y-1)\ln 2$ with $N_y$ 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.