Negativity spectrum in 1D gapped phases of matter

Understand

We investigate the spectrum of the partial transpose (negativity spectrum) of two adjacent regions in gapped one-dimensional models.

• We show that, in the limit of large regions, the negativity spectrum is entirely reconstructed from the entanglement spectrum of the bipartite system.
• We exploit this result in the XXZ spin chain, for which the entanglement spectrum is known by means of the corner transfer matrix.
• We find that the negativity spectrum levels are equally spaced, the spacing being half that in the entanglement spectrum.