Fourier-space entanglement of spin chains

作者：Ibanez Berganza Miguel; Rodriguez Laguna Javier^*; Sierra German

来源：Journal of Statistical Mechanics: Theory and Experiment , 2016, 2016(5): 053112.

DOI：10.1088/1742-5468/2016/05/053112

• entanglement in extended quantum systems (theory)
• quantum phase transitions (theory)
• spin chains
• ladders and planes (theory)
• Luttinger liquids (theory)

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 of 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 lies at the origin of the success of the renormalization techniques in momentum space.

• 出版日期2016-5