Fourier-space entanglement of spin chains

TL;DR

This paper investigates momentum-space entanglement in spin chains, revealing how anisotropy and phase transitions influence entanglement patterns, with implications for renormalization techniques.

Contribution

It provides a detailed analysis of Fourier-space entanglement in various spin models, highlighting phase transition signatures and entanglement scaling behaviors.

Findings

Entanglement occurs between opposite momenta in XY and ITF models.

Anisotropy induces entanglement in momentum pairs.

Entanglement entropy grows logarithmically with system size in XXZ model.

Abstract

Entanglement between different regions in momentum space is studied for ground states of some spin-chain Hamiltonians: the XY model, the Ising model in a transverse field (ITF) and the XXZ models. In the XY and ITF cases, entanglement only takes place between states with opposite momenta. Thus, an anisotropy in the interaction induces entanglement in the momentum pairs. In the ITF case, the ferromagnetic phase is characterized by a total entropy between left- and right-moving modes which is independent on the external field. This result characterizes the Ising phase transition in momentum space. In the critical XXZ case, we provide evidence that the maximal entropy between energy modes around the Fermi point grows logarithmically with the system size, with a prefactor which depends on the compactification radius. The slow growth of the entanglement in Fourier space with the system size provides an explanation for the success of the renormalization techniques in momentum space.