Entanglement and corner Hamiltonian spectra of integrable open spin chains

Abstract

Entanglement spectra (ES) for the critical SU(N) (2 <= N <= 4) spin chains and other integrable models of finite length are studied with the density matrix renormalization group method. For all models under investigation, the level spacings and the degeneracy structure of the ES are in excellent agreement with the spectra of the corner Hamiltonian, defined as the generator of the associated corner transfer matrix. The correspondence holds between the ES (n) at the n-th cut position from the edge of the spin model, and the corner Hamiltonian of length n, for all small values of n. The cut position dependence of the ES shows a period-N oscillatory behavior for a given SU(N) chain, reminiscent of the oscillatory part of the entanglement entropy observed in the past for the same models. 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. Heuristic argument based on Young tableaux consideration can explain the period-N structure of the ES qualitatively.