Entanglement and corner Hamiltonian spectra of integrable open spin chains

Abstract

We investigate the entanglement entropy (EE) and entanglement spectra (ES) of critical $\mathrm{SU}(N) (2\ensuremath{\le}N\ensuremath{\le}4)$ spin chains and other integrable models of finite length with the density matrix renormalization group method. For all models under investigation, we find a remarkable agreement of the level spacings and the degeneracy structure of the ES with the spectrum of the corner Hamiltonian (CS), defined as the generator of the associated corner transfer matrix. The correspondence holds between ${\mathrm{ES}}^{(n)}$ at the $n\mathrm{th}$ cut position from the edge of the spin model, and the spectrum ${\mathrm{CS}}^{(n)}$ of the corner Hamiltonian of length $n$, for all values of $n$ that we have checked. The cut position dependence of the ES shows a period-$N$ oscillatory behavior for a given $\mathrm{SU}(N)$ chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. However, the oscillations of the ES do not die out in the bulk of the chain, in contrast to the asymptotically vanishing oscillation of the entanglement entropy. We present a heuristic argument based on Young tableaux construction that can explain the period-$N$ structure of the ES qualitatively.