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We study the momentum space entanglement spectra of bosonic and fermionicformulations of the spin-1/2 XXZ chain with analytical methods and exactdiagonalization. We investigate the behavior of the entanglement gaps, presentin both partitions, across quantum phase transitions in the XXZ chain. In bothcases, finite size scaling reveals that the entanglement gap closure does notoccur at the physical transition points. For bosons, we find that theentanglement gap observed in [Thomale et al., Phys. Rev. Lett. 105, 116805(2010)] depends on the scaling dimension of the conformal field theory asvaried by the XXZ anisotropy. For fermions, the infinite entanglement gappresent at the XX point persists well past the phase transition at theHeisenberg point. We elaborate on how these shifted transition points in theentanglement spectra may in fact support the numerical study of physicaltransitions in the momentum space density matrix renormalization group.

Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions