Entanglement generation resonances in XY chains

TL;DR

This paper investigates how entanglement in XY spin chains exhibits resonant peaks influenced by magnetic fields and anisotropy, providing analytical and exact results for small and finite chains.

Contribution

It reveals the non-monotonous, resonant behavior of entanglement maxima in XY chains, with analytical solutions and exact results for finite chains.

Findings

Maximum entanglement shows resonant peaks as a function of magnetic field.

Peak width is proportional to anisotropy and height remains finite at low anisotropy.

Pairwise entanglement can exhibit narrow peaks above plateaus in small chains.

Abstract

We examine the maximum entanglement reached by an initially fully aligned state evolving in an XY Heisenberg spin chain placed in a uniform transverse magnetic field. Both the global entanglement between one qubit and the rest of the chain and the pairwise entanglement between adjacent qubits is analyzed. It is shown that in both cases the maximum is not a monotonous decreasing function of the aligning field, exhibiting instead a resonant behavior for low anisotropies, with pronounced peaks (a total of [n/2] peaks in the global entanglement for an $n$-spin chain), whose width is proportional to the anisotropy and whose height remains finite in the limit of small anisotropy. It is also seen that the maximum pairwise entanglement is not a smooth function of the field even in small finite chains, where it may exhibit narrow peaks above strict plateaus. Explicit analytical results for small chains, as well as general exact results for finite n-spin chains obtained through the Jordan-Wigner mapping, are discussed.