Entanglement of magnon excitations in spin chains

TL;DR

This paper calculates the entanglement of magnon excitations in integrable spin chains, revealing a decomposition into free fermionic or bosonic states and proposing a classification scheme in the scaling limit.

Contribution

It provides an exact calculation of magnon entanglement in spin chains and introduces a classification approach for entanglement in free fermionic and bosonic Hamiltonians.

Findings

Entanglement decomposes into free particle states for small magnon numbers.

Conjecture on classifying entanglement in free fermionic and bosonic Hamiltonians.

Results classify entanglement in a broad class of integrable spin chains.

Abstract

We calculate exactly the entanglement content of magnon excited states in the integrable spin-1/2 XXX and XXZ chains in the scaling limit. In particular, we show that as far as the number of excited magnons with respect to the size of the system is small one can decompose the entanglement content, in the scaling limit, to the sum of the entanglement of particular excited states of free fermionic or bosonic theories. In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be also classified, in the scaling limit, with respect to the entanglement content of the fermionic and bosonic chains with the number operator as the Hamiltonian in certain circumstances. Our results effectively classify the entanglement content of wide range of integrable spin chains in the scaling limit.