Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions

TL;DR

This paper analyzes the momentum space entanglement spectra of bosonic and fermionic spin chains, revealing that entanglement gap closures do not align with physical phase transitions and depend on the system's conformal field theory properties.

Contribution

It provides a detailed study of entanglement gaps in momentum space for bosons and fermions, showing their behavior across phase transitions and dependence on conformal scaling.

Findings

Entanglement gaps do not close at physical transition points.

Bosonic entanglement gap depends on conformal field theory scaling dimension.

Fermionic entanglement gap remains large past the phase transition.

Abstract

We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both partitions, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling reveals 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 XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may in fact support the numerical study of physical transitions in the momentum space density matrix renormalization group.