Entanglement spectra of Heisenberg ladders of higher spin

Abstract

We study the entanglement spectrum of Heisenberg spin ladders of arbitrary spin length S in the perturbative regime of strong rung coupling. For isotropic spin coupling the entanglement spectrum is, within first-order perturbation theory, always proportional to the energy spectrum of the single chain with a proportionality factor that is also independent of S. In particular, although the spin ladder possesses an excitation gap over its ground state for any spin length, the entanglement spectrum is gapless for half-integer S and gapful otherwise. A more complicated situation arises for anisotropic ladders of higher spin S ≥ 1 since here even the unperturbed ground state has a nontrivial entanglement spectrum. Finally we discuss related issues in dimerized spin chains.