Abstract
We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin- chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the anisotropy. For fermions, the infinite entanglement gap present at the point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.
- Received 13 May 2014
DOI:https://doi.org/10.1103/PhysRevLett.113.256404
© 2014 American Physical Society