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.
Highlights
Entanglement between subsystems in extended many-body systems has become one of the key ingredients to understanding of quantum matter [1,2,3,4,5]
In addition we conjecture that the entanglement content of the generic translational invariant free fermionic and bosonic Hamiltonians can be 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
A quantitative characterization of quantum entanglement is the entanglement entropy and it is defined as follows: for a quantum system in state |K, one can divide the whole system into two subsystems A and B, integrate out the degrees of freedom of the subsystem B of the total system density matrix ρK = |K K|, and obtain the reduced density matrix (RDM) ρA,K = trBρK of the subsystem A
Summary
Entanglement between subsystems in extended many-body systems has become one of the key ingredients to understanding of quantum matter [1,2,3,4,5]. We first make a conjecture that the results presented in [52, 54] are valid for non-coupled systems, i.e. the Hamiltonian being just the totally free number operator, and for generic translational invariant free fermionic and bosonic chains as far as the extra momenta are big. In particular there are a few novel results in those appendices including the analytical and numerical calculations of the entanglement entropy, beyond the Rényi entropy with integer index n ≥ 2, from the subsystem mode method in the free fermions and free bosons in appendices B and C and the analytical expression of various limits of the Rényi and entanglement entropies in the two-magnon bound states of the XXX chain in appendix D
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